Yes, you can take higher-level Stances at your first class level

There are several issues here.

First of all, this line is in the form of a descriptive statement, not a prescriptive one: it describes the usual case of things, rather than defining a limitation on your options. I would argue that it is there solely to help players new to the book, who are creating their first martial adept from level 1.

After all, a great many statements are made in Wizards’ products that assume you are single-classed, and starting from ECL 1 is the default assumption for the game. The Wizard’s Specialization feature says you cannot cast spells from your banned schools – but you actually can, you just need to get that ability from another class.

In addition, the line does not say “first-level martial adepts are restricted to 1st-level Stances.” It says that they “begin play” with a single 1st-level maneuver. A multiclass character taking his first level in a martial adept class after ECL 1 is not “begin[ning] play,” so the statement does not apply to him.

For that matter, taken literally, that would imply that any martial adept has only a single 1st-level Stance when the game starts – even if he started at level 20 and took Martial Stance feats repeatedly. Clearly, this is not the case, which is only further evidence that the line is not a rule, but a hint or (supposedly) helpful description.

Finally, if you rule that it does prevent higher-level Stances from being taken for your first class level, it flies in the face of the entire Tome of Battle design pattern. Tome of Battle was intentionally designed to mesh well with previous books and existing characters – that is why the Initiator Level rules were written the way they were in the first place.

Every single other method of learning any maneuvers – Stances included – allows those with higher Initiator Level to “skip” lower-level maneuvers – because Wizards finally understood how important it was to the system that characters be getting level appropriate class features, even if they multiclass. For instance, a 12th-level character, with no martial adept levels, still has an Initiator Level of 6, and can take Martial Study or Martial Stance to get a 3rd-level maneuver or stance, respectively.

This single supposed exception does not make any sense in light of the context that Tome of Battle provides, does not have the form of a prescriptive rule, and does not actually specify your first martial adept level but rather whether or not the character is “beginning play,” which really does not make much sense if taken literally.

First of all, the Prestige Class Tier List is not nearly as widely-ascribed-to as JaronK’s base class one. For one thing, it is much harder to judge a prestige class (especially ones that can vary so much depending on how you enter), and for another there are just so many more of them.

Take the Shadowsun Ninja. For a Monk, it’s a dramatic step up; for a Swordsage, it’s... a thing. There are some neat tricks possible with it (Tomb-Tainted Soul or the Undead type allow you to use the negative energy for healing while using the positive energy on your allies, so that’s indefinite healing), but ultimately it doesn’t really change much about the Swordsage’s tier.

The problem of the Master of Nine is that it requires a ton of feats. If you aren’t a Swordsage, it also requires multiclassing, but that’s not really a bad thing for initiators. In fact, judicious multiclassing helps a great deal with the feats, because one level in Cleric gets you two of the feats (Darkness or Shadow domain gets Blind-fight, Time domain gets you Improved Initiative). The unarmed Swordsage adaptation also gets you Improved Unarmed Strike, and most Swordsages want Adaptive Style anyway.

That leaves only Dodge to be picked up. Several options, including Tome of Battle’s own Desert Wind Dodge, are better than ordinary Dodge, though even the best is still weak. Still, one feat burned and the single-best-dip-in-the-game (don’t forget that Cleric 1 also gives a few spells, and Turn Undead can be used to fuel the often-excellent [Divine] and [Domain] feats) is not too high a price to pay for the excellent class features that Master of Nine offers.

The limited Dual Stance feature is not nearly as good as the Warblade’s version of the same, but it’s still awesome and you can get it way sooner than 20th level. The eight maneuvers in five levels, of course, is phenomenal, and a maneuver readied per level is insane.

If you try to get into Master of Nine as a regular, single-classed Swordsage, you’re making a huge mistake and will regret burning all of your feats that way. If you’re clever about picking up feats, though... the class can be excellent.

Side-note: you don’t lose “more” by taking another level in addition to Cleric 1 with your Swordsage levels, because other class levels count half for your initiator level. There are a lot of great options for that extra level. Fighter or Psychic Warrior could be used to get another feat, to make up for the one lost picking up (Desert Wind) Dodge. Psychic Warrior also grants you a single power – which could be expansion, for instance, a great choice. Barbarian gives a ton of stuff on level 1 as well (don’t forget to check the various alternatives for Rage for the one that best works for you).