Exactly. People can be unbelievably obtuse when it comes to remarks the opposition makes while simultaneously showing remarkable skill in finding exculpatory facts for their own side. The media is especially guilty of sensationalizing what would otherwise be mundane statements into controversy. An example of this would be taking the phrase "you people" out of context and turning into a racial/etc issue when the intent was never there to begin with.

I'd disagree and say "you people" is a pretty blatant one. It communicates pretty clearly an intent to paint with a really really wide brush.

So if a manager says to the office, "Some of you people need to improve your performance" and one person takes that as meaning only people of color need improvement and reports the manager, you would side with the employee?

There are many common cases where someone refers to a group of people with the intention of meaning everyone while someone in the group interprets it as referring to a subset of the group. It stems from the ambiguity of the word people and the impact of tone and body language in conveying its ultimate meaning.