Your stubbornness makes it less likely people will take you seriously on anything, Large. If all you have to say is "reread the thread," go suck on a pacifier or something.
Technically, none of the definitions of the word "ability" allows for a cleric with Anyspell to qualify. All of these allow the wizard to qualify, even when out of spells. It's simple reading comprehension.
1. The quality of being able to do something, especially the physical, mental, financial, or legal power to accomplish something.
The wizard inherently has the physical and mental quality of being able to cast spells, always. Number of spells per day is none of the physical, mental, legal, or financial power to accomplish casting spells, it is an abstract game rule dis-joined from the above. The cleric with Anyspell only gains the physical and mental power to accomplish casting arcane spells by first taking an action which grants the quality itself. If Anyspell is not currently active, the cleric has neither and thus does not qualify.
2. A natural or acquired skill or talent.
A wizard always has the natural acquired skill to cast arcane spells, regardless of whether he has a spell of a particular level available to cast that day. He still retains the quality. The cleric only gains an acquired skill to cast arcane spells by first casting Anyspell.
3. The quality of being suitable for or receptive to a specified treatment; capacity
This obviously refers to the following definition of "capacity:"
a : an individual's mental or physical ability
The wizard has both the mental and physical ability to cast arcane spells, even with none left for the day. Whether he can or cannot do it "right now" is not relevant, because he inherently owns this ability.
The cleric, on the other hand, must first take an action that gives him the ability. He does not inherently own it. Rather, he gains it through magic, and loses it once that magic is expended.
It is a question of degrees of separation, not a question of "can I do it right now." The cleric with Anyspell is separated from the ability to cast arcane spells by a single degree of separation, Anyspell. The wizard is separated by none, he has the ability inherently. Without Anyspell, the cleric cannot cast arcane spells, period. The wizard needs no qualification action, he has the ability inherently whether or not he has any spells left for the day. Spells per day is not a reflection of owning the ability, it is an abstraction of the wizard's limitations and nothing more.
If you want to ignore the definitions of words, be my guest. It just makes you look like a boob.