However, look at the individual classes. Wizard has the Spellcasting ability, which allows it to cast Arcane spells. This ability sets a number of time each level of spell is cast based on class level. The ability to cast the spells is still present, even if you are out of your daily allotment.
This is not true for the Anyspell using cleric. He does not have the ability to cast Arcane spells. Anyspell, arguably, grants him the ability to do so.
Character A is a Wiz3/Cleric3. He has the ability to cast cleric and wizard spells of 2nd level. His classes say so. He is out of spells today, but he still has the ability to do it.
Character B is a Cleric 6. He is planning on using Anyspell to get into his prestige class. Unfortunately, on Tuesday he needs to use a different spell, and is unable to cast Anyspell to give him the ability to cast Arcane. He no longer qualifies for the class, until he again casts Anyspell.
Character B is the same as someone using a Ring of Evasion to get into a class requiring evasion. It works as long as the ring is on the guys finger. However, if the ring is stolen, lost, destroyed, whatever, he no longer qualifies. Same with B. B no longer has the ability to cast those Arcane spells. If he gets the ability back later, either by taking Wiz levels for example or by recasting Anyspell, then he once again qualifies.