I read things online all the time that I'm pretty sure are, at best, wild exaggerations of the truth (on this forum a lot...especially when people come back to 'clarify' a post). Many times, it seems that people make up these stories/points to emphasize their own arguments or way of thinking. As hard as it is, I try my best to just let them go (not always successful, but I do try). Because exposing them as liars usually just starts an argument that I have no interest in getting into. I think it's fine to ask clarifying questions and I also think it's even ok to have an honest reaction...like "wow! That sounds so crazy...it's hard to believe!"
There are attention-seekers online and there are people that lie, I believe, because they just can't help it. I might choose not to take their advice, jump to their rescue, take them at their word, get sucked into their latest wild story etc, but I do know that trying to make them admit to their lie is an exercise in futulity. Is it rude to imply they are lying...I don't know. I think it's rude to outright lie for no other reason than to make yourself look good or try to "win" a discussion so I think it's a bit hypocritical for a "liar" to state that we can't question their stories. At the same time, some hard to believe stories are in fact true and it's difficult to verify facts online sometimes, so it's kind of hard to 'expose' someone factually even if your gut is telling you they are full of it. Most of the time I just resign myself to the fact that there are those who have credibility with me and those who don't. I react to each differently.