If a college/ university made false claims on its website, should you still consider studying there?
Are you sure this isn't a mistake or misunderstanding from either the university or the association?

I would recommend contacting the department or university. I try to give people the benefit of the doubt with this type of thing but are you sure this is a reputable school? Accreditation is a vague thing and varies wildly in how it is regulated and who accredits it, especially across different countries. 

I'm a little surprised that you contacted the association directly. I myself never pay attention to professional associations and don't know anyone who does (at least not enough to investigate the claim). 

But again, if this is important to you, I would recommend giving the university a chance to clarify by contacting them. You must remember, the people making the website or handling the accreditations most likely aren't the professors teaching the courses. I would also recommend looking into the reputation of this university more if this is indeed true.

EDIT: Many diploma mills/for-profit schools are "accredited" but that doesn't mean they are reputable, so beware.