The Olbers' paradox is from the 1800s, before we knew about the expansion of space. It's arguing against a static, infinitely old universe. As you point out, we now know that this isn't the case.
The paradox says that an universe infinite in space and time would have to be bright in all directions. By infinite in time, I mean that the universe has been around infinitely long, i.e. it has no beginning. The finite speed of light wouldn't matter here since the light would have had an infinite amount of time to reach you.
I want to clarify the scope of this advice. If I've actually committed a crime and a cop is interrogating me about it, I should shut up and talk to my lawyer. (e.g. I robbed someone's house) In the other extreme, if someone's committed a crime against me, I should actively call the police to talk to them (e.g. someone robbed my house).
The majority of interactions with police fall somewhere between these two examples in terms of susceptibility. What determines when I should be talking to the cops and when I shouldn't?