The most likely interpretation is that if an item states that it cannot be removed without remove curse, then it cannot be removed without remove curse.

Reason 1: Specific beats general

The principle of "specific beats general" is stated as follows in the Rules Compendium (2007):

A general rule is a basic gudeline, but a more specific rule takes precedence when applied to the same activity. For instance, a monster description is more specific than any general rule about monsters, so the description takes precedence.

While dispel magic in general can suppress magic items, specific cursed items can override this with specific properties.

Reason 2: Item descriptions

Cursed items are usually explicit when naming the spells which will counter their curse. For example, consider the Gauntlets of Fumbling (emphasis mine):

Once the curse is activated, the gloves can be removed only by means of a remove curse spell, a wish, or a miracle.

The item text is very specific: the item cannot be removed, except by one of the three named spells. It does not say what happens when you try any other method or spell, only that it will fail.

Note that this particular curse only prevents removing the item. It may still be possible to temporarily dispel a cursed item's other magical properties.

Reason 3: Primary source rule

According to the D&D 3.5 errata, when two rules come into conflict, the Dungeon Master Guide takes precedence over the other rulebooks when it comes to rules for magic items and cursed items, since the DMG is the primary source for those rules.

(However, this is not a watertight argument, since by the same token, the Player's Handbook is the primary source for rules on spells, such as dispel magic.)

Reason 4: Adjudication by similar rules

The Dungeon Master's Guide gives the following advice to DMs adjudicating ambiguous situations:

When you come upon a situation that the rules don't seem to cover, consider the following courses of action:

• Look to any similar situation that is covered in a rulebook. Try to extrapolate from what you see presented there and apply it to the current circumstance.

In other words, it's reasonable for a DM to interpret an ambiguous rule by inferring a solution from other related rules. The closest similar situations I can find are as follows:

• The spell bestow curse says that "the curse bestowed by this spell cannot be dispelled". This supports the idea that curses are specially resistant to dispel magic.
• The Loadstone, a cursed item, will return to your possession even if you destroy or throw it away. This suggests that even if you temporarily outsmart a cursed item, it will return.

Identifying spell effects currently affecting an item/creature or spell origins of an item, learning the number of charges of a magic item, and dramatically reducing the time expense.

You can use the identify spell to identify any spell effects an item or creature is currently being affected by or the spell used to create an item (see the spell description from the SRD or PHB).

You learn whether any spells are affecting the item [you touch throughout the casting] and what they are. If the item was created by a spell, you learn which spell created it.

If you instead touch a creature throughout the casting, you learn what spells, if any, are currently affecting it.

The short rest option for identifying the behavior of magic items does not replicate the options above, since the short rest option only applies to magic items (and, depending on how the rules are interpreted, maybe even only those that require attunement).

In addition, you learn how many charges a magic item has.

If [the item you touch throughout the casting] is a magic item or some other magic-imbued object, you learn its properties and how to use them, whether it requires attunement to use, and how many charges it has, if any.

The short rest option makes no mention of learning the number of charges, although it is common for a DM to rule otherwise (see the description of this activity in the Magic Items, Attunement section of the rules from the SRD or DMG).

[A]t the end of the short rest, the creature gains an intuitive understanding of how to activate any magical properties of the item, including any necessary command words.

Finally, the above advantages are in addition to the reduced expense of time. In order to use the short rest option to learn a magic item's properties and also become attuned to it, you actually have to spend 1 short rest learning its properties and then another becoming attuned.

Attuning to an item requires a creature to spend a short rest focused on only that item while being in physical contact with it (this can't be the same short rest used to learn the item's properties).

That's a total of 1 hour of resting to learn some of its properties (or 2 hours if you also want to become attuned), as opposed to a 1 minute casting time to learn all of its properties (or 1 hour and 1 minute if you also want to become attuned). Since identify is a ritual, it can also be cast in 11 minutes without expending a spell slot.