My family is Hispanic, and all are citizens or legal immigrants. But we find the term "illegal" to be a bit harsh and prefer "undocumented".
And I prefer the term "wildly successful and rich famous talk show host with a supermodel wife and NFL cheerleader mistress". Instead I get "small market AM station morning host that drives a 10 year old car". Because it's more accurate.
I know the AP style book (and all the rest, I'm sure) prefer the politically correct term for illegal immigrants, but that doesn't make it any more right.
And I'm not even IN the "deport them all" crowd, since that's impossible and stupid. I just like to use the best words to describe whatever I'm talking about. If someone is offended at being called an illegal immigrant, maybe they should have come here legally. If someone is here legally, the term doesn't apply to them. No offense should be taken.
Since you used the analogy of speeding, if I get caught speeding, I wouldn't be offended a bit if someone calls me a speeder. If I got caught peeking in the neighbor's window, I would have no room being offended if someone called me a peeping Tom.