How much do AP Scores matter for top schools?

I don’t think I’d go as far as saying they’re nearly irrelevant. Stanford’s wording is correct - they rarely play a “significant” role. Many other things are more important. But they are additional data points that show mastery of material and readiness for college. Yes, an application with eight 5’s on APs would be more attractive than one without. But the incremental improvement is small (but not zero)