With evidence? I mean logically think about it. A good player is still going to be a good player in the clutch. They aren't suddenly a better player then. On the other hand you're not surprised when Darwin Barney does nothing in a clutch spot.
Just googling best clutch hitters gives me the following link
Miguel Cabrera(career .320/.397/.563)
Mike Trout(.306/.396/.550)
Andrew McCutchen(.298/.385/.497)
Giancarlo Stanton(.271/.365/.539)
David Ortiz(.285/.379/.546)
Pablo Sandoval(.294/.346/.464)
Buster Posey(.309/.375/.487)
Robinson Cano(.309/.358/.499)
Paul Goldschmidt(.293/.383/.525)
Joey Votto(.311/.417/.535)
Troy Tulowitzki(.300/.374/.518)
Victor Martinez(.306/.373/.474)
Jose Abreu(.314/.381/.581)
Matt Carpenter(.293/.379/.432)
Jose Altuve(.301/.339/.399)
Aramis Ramirez(.285/.343/.496)
The *worst* player on that list average wise is Giancarlo Stanton who's a 2x All-Star and 1x Silver Slugger at 25. The worst in terms of OBP is Altuve who's a 2x All-Star and 1x Silver Slugger at 24. The point here isn't that these players are bad in high leverage situations. The point is they are good players regardless of the situation. My point here is it's not like people are saying Andrelton Simmons is a great clutch hitter(career .251/.296/.371).