I cannot possibly the only person who cringes when hearing the phrase "trust the evidence". What an absurdly anti-scientific statement! Also, evidence doesn't say anything at all, of course. We try to build an explanation of data, and you know what the scientific community does with those explanations? They try to demolish your precious idea! If you won't do it, someone else will make their career tearing it to bits. It's a brutal world out there, and the only thing making evidence-based explanations even remotely trustworthy is the fact that other people out there can totally destroy your career forever, and pull themselves up on top of the pile of corpses, by showing it was wrong. Of course so few researchers blatantly misrepresent data – it's a brutal enough ecosystem that they'd be immolated and eaten for dinner if they did.
I think what people generally mean when they say things like "trust the evidence" is: be reasonably persuadable. If you aren't reasonably persuadable, people simply won't find your insights useful. They probably aren't. You won't get cited. You won't get funding. That's the scientific model.
But also, just while you're living life, it seems like a virtue. Be persuadable, within reason. Have an idea of what you're looking for, when you find the answer to a question, and let your conclusion be pushed around by the data. Of course, you have to ask the questions yourself – otherwise you're just being pushed around by innuendo and suggestion. Someone could fill your head with incorrect models by only telling you truths! So, make sure to ask excellent questions, and make sure those questions are ones where you're open to being persuaded. Have a differential response to reality.