Insight doesn't exactly "count as evidence". Rather, when you acquire insight, you improve the evidence-strength of the best algorithm available for assigning hypothesis probabilities.

Initially, your best hypothesis-weighting algorithms are "ask an expert" and "use intuition".

If I give you the insight to prove some conclusion mathematically, then the increased evidence comes from the fact that you can now use the "find a proof" algorithm. And that algorithm is more entangled with the problem structure than anything else you had before.