I am not giving legal advice or opinions, but as a general rule, a diver, whether OW or an instructor, is not going to be held liable for an injury to someone who is on the same boat or even the same group unless he or she has specifically engaged in affirmative conduct that would give rise to liability. That might include giving advice about diving or telling the diver not to worry because you are an instructor.
The reality is that general rule or not, if you say or do something really stupid, you could end up being held liable anyway. Being an arrogant jerk on the witness stand is one good way. Being perceived as a liar is another. I have seen it happen many times.
A skilled lawyer will try to manufacture a basis liability if there isn't actually one. (That's his or her job, what the rules call for and what the client wants, so don't blame the lawyer.) IMHO, if there is no other basis for liability and a diver has hidden his or her true cert level, that would be one of the places I'd expect a lawyer to look to manufacture liability. The questions I asked above might be sufficient to get a jury thinking that the defendant was hiding his or her cert level to avoid liability because he or she knew he or she had a duty and did not want to shoulder it.
DO NOT ANSWER THE FOLLOWING QUESTION IN PUBLIC ... but ... isn't that really at least one reason why people are concerned about disclosing their real cert level?
Now, for anyone who said "no," go back and re-read this whole thread.
BTW: Experts in criminal law will tell you never to talk to the police. They will tell you that even if you are telling the truth, if someone else says something contradictory, the police may use the inconsistency against you. At a minimum, they might decide to scrutinize you further. However, if you say nothing, there is no inconsistency. And, you have a nearly absolute right to remain silent.