Seriously, and according to its own texts, Wizards of the Coast says

The Rules Compedium Can't Change the Core Rules

I know it's weird. I know it sounds like nonsense. I know that when the core rules were published things like swift actions didn't exist. I have shed blood on the Internet battlefield between the Rules Compendium declaring free actions are only available on one's turn versus the Player's Handbook slightly vague addressing of the topic, especially in conjunction with immediate actions. I know. I know.

Wizards of the Coast Created a Flawed Paradigm
Here's the skinny: All of the errata documents have this Errata Rule describing Primary Sources

When you find a disagreement between two [Dungeons and Dragons] rules sources, unless an official errata file says otherwise, the primary source is correct. One example of a primary/secondary source is text taking precedence over a table entry. An individual spell description takes precedence when the short description in the beginning of the spells chapter disagrees.

Another example of primary [versus] secondary sources involves book and topic precedence. The Player's Handbook, for example, gives all the rules for playing the game, for playing PC races, and for using base class descriptions. If you find something on one of those topics from the Dungeon Master's Guide or the Monster Manual that disagrees with the Player's Handbook, you should assume the Player's Handbook is the primary source. The Dungeon Master's Guide is the primary source for topics such as magic item descriptions, special material construction rules, and so on. The Monster Manual is the primary source for monster descriptions, templates, and supernatural, extraordinary, and spell-like abilities.

Emphasis mine. So the most recent publication of the core rules--the 2013 editions of the Player's Handbook, Dungeon Master's Guide, and Monster Manual--are absolutely primary, even if topics within those texts were subtly changed, outright contradicted, or the subject of FAQ or game designer commentary by other texts between 2000 and 2013 before those texts' publications, and even if uncorrected errors remain in any of the most recently published core books that were corrected by other books before the core rule' republication.

Flaws other books set right may have been backwardly-uncorrected--or whatever Orwellian phrase you might want to use--by the republished core rules.

The Rules Compendium Asserts Its Own Primacy
The Rules Compendium's Introduction says

When a preexisting core book or supplement differs with the rules herein, Rules Compendium is meant to take precedence. If you have a question on how to play [Dungeons and Dragons] at the table, this book is meant to answer that question.

So while the Rules Compendium is meant to take precedence, it, officially, can't.

Why Reject the Rules Compendium?

Some folks enjoy playing by the rules--the rules are there, someone was paid to write them, and some (probably) paid to acquire them--, and having the core rules changed by a source and only that source makes them uncomfortable, like somebody's trying to pull a fast one. Some of the Rules Compendium's so-called clarifications are outright changes to the rules, and that bugs folks.

Examples of changes implemented by the Rules Compendium include...

• Charging through Hindrances: The PH says, "You must have a clear path toward the opponent, and nothing can hinder your movement (such as difficult terrain or obstacles)" (154) then goes on to define a clear path as empty of such things as opponents and allies. The RC allows the use of some skills to avoid movement hindrances during a charge (27).
• The Action Needed to Activate Some Magic Items: The DMG says that activating of spell completion and spell trigger magic items "is a standard action" (213). The RC, says, "Activating a spell trigger [or spell completion] item takes the same amount of time as the casting time of the spell that the item stores" (85).
• The Survival DC for Avoiding Quicksand: The original Survival skill check DC for avoiding quicksand is 8 (DMG 88). The Rules Compendium on page 103 increases this DC to 15 without commentary.
• Touch Spells and Threatening an Area: The PH is unclear on whether a creature who lacks the feat Improved Unarmed Strike, a natural weapon, or both threatens an area with a touch spell's held charge (PH 141-2). The RC puts forth decisively that "a spellcaster delivering a touch attack spell... count[s] as armed. Being armed in this way counts for both offense and defense. So a creature armed in this way can make attacks of opportunity, and such a creature doesn’t provoke attacks of opportunity when attacking" (16).
• Using the Skill Sleight of Hand: The rules for the skill Sleight of Hand are on PH 82. The RC maybe expands but possibly replaces this description on page 117, yet the RC excludes the entries Action, Try Again, Special, Synergy, and Untrained present in the PH. Some RC changes go unmentioned in the text yet appear on the nearby table (e.g. a creature suffers a -20 penalty when taking a move action to make a Sleight of Hand skill check). Whether the RC's Sleight of Hand skill description is to supersede or supplement the PH description is unmentioned by the text.
• What It Means to Be Hidden: Using the PH alone, the only effect of being hidden while in combat (beyond being undetected) is the possibility of combat ending to take advantage of a future surprise round. This is substantially changed by the RC's description of the skill Hide (92).
• When Daily-use Items Recharge: The core rules don't provide a general rule for a magic item (or, for that matter, any special ability) with 1 or more abilities usable per day to regain its uses of those per-day abilities, necessitating house rules. The RC addresses the recharge rate for daily-use magic items that don't otherwise provide them on page 86.

"This is Bizarre! Can I read more?"
Sure. Giant in the Playground forums' Curmudgeon is probably the most articulate and vociferous proponent of the Rules Compendium's flawed existence. His comments here summarize his stance well, and it's a good read.

Note: I'd like to make this answer a repository of links to questions and answers that demonstrate where the core rules and RC differ. You can add such into the Examples of changes... yourself or leave a Comment.

The Specialty is purely flavor, and doesn't provide any mechanical benefit. The knowledge that a Sage provides isn't meant to be practical knowledge, but more scholarly.

For example, a professor of anatomy might know the name of every single bone in your body, but that doesn't necessarily mean that he'd be any help setting a broken bone. In the same way, you might be a Sage specializing in Alchemy, but that doesn't mean that you've spent years mixing and testing chemicals. It means that you've spent years reading theoretical papers and reports from actual alchemists.

If someone wants to find the recipe for transmuting lead into gold, you might be able to help them or at least point them in the right direction, but if someone comes to you with the esoteric materials required to actually pull that off, you wouldn't have the expertise needed to mix the chemicals with the precision necessary to not blow yourself up or fill the room with noxious fumes.