Technically, the answer is correct, in that, if a church is indeed a group of people, and the meaning was limited to just that.
The problem is that the terms, in typical understanding, are interchangable. So when a person says "I'm going to chruch", they usually mean that they are attending a religious service that involves a group of people coming together at a given location to worship.
We all know the real reason that they don't call it a church, which has already been mentioned. Can't be like that dirty old gal Christendom now, can we?