Yep, the word "support" is probably the most misused word in tech support, in my experience. Even the people who use it frequently don't understand what they are saying.

What it usually means is, "hey, you may be able to do that, and more power to you if you do, but we aren't going out of our way to help you and we take no responsibility for how well you do it."

People misinterpret it thus: "well, you don't support it, so you obviously oppose it," like we were talking some sort of political process. It doesn't mean that. Often, technicians themselves use this line of reasoning to chase away people who are trying to do something, like "we told you we don't support that, and if you are having problems now, it's your own fault" as if people trying to do it are somehow immoral.

Users who do something that isn't supported are perfectly free to do so, but they can't expect help from a company that has announced that it won't help. That is all that "we don't support that" means.