I'm not sure that anyone is trying to equate plausibility with evidence of the actual claim, but merely explain that not all claims are equal and some are more plausible than others. The fact is that if a friend of yours casually dropped into conversation that they went for a ride on a bike the other day, you would automatically believe them without requiring any kind of verification. Whereas, if that same friend casually dropped into conversation that they went for a ride on the back of dragon the other day, you'd probably make a confused face and ask them to repeat themselves.
This is because not all claims were equal. Even in a case where you have no evidence for either claim, your logical mind still dictates that one claim is plausible to the point that it doesn't require evidence to believe at face value, while another claim is so implausible that you simply cannot believe it at face value. It's perfectly possible that your friend could be lying to you about riding a bike, but believing that lie doesn't make you stupid or gullible - it just makes sense, based on everything you know about bikes and riding them, that riding a bike is not an exceptional claim and does not require much, if any, investigation.
At least, that's the point I'm trying to make.