[AppyPappy]

It doesn't make sense. They mean "I won't". Of course they can.

[solsrchr2]

I usually keep my religion to myself. Everyone I work with can tell I am Christian by the picture of Jesus in my cube. I don't generally tell people I'm a member of The Church of Jesus Christ of Latter Day Saints (Mormon). I have never said I can't do anything because I'm a Mormon. People who ask me if I want a drink I tell them I'm allergic. That when I drink I break out. You know, windows, doors, and teeth. That usually stops any further offers of alcohol.
The LDS church is very conscious of their image and try to keep a low profile. If an ad just implies the wrong message, it would be pulled.

[Prime Choice]

It doesn't make sense. They mean "I won't". Of course they can.

Yep. People often confuse "can't" for "won't." Sort of like the way Leftists confuse freedom of speech (which they demand) with freedom of thought (which they abhor).