Well, that does depend on "in whose field of expertise the point of contention is". If a professional statistician says that a particular study screwed up its statistical analysis, I have little reason (ceteris paribus) to disbelieve him. That, of course, doesn't mean the paper should go into the wastebasket, maybe it just needs a minor correction -- but it's very hard to generalize about such things.

Certainly, when statisticians start to talk about, say, biology, you should be suspicious -- but no more than you should be suspicious of climate scientists talking about economics.