It's a simplification. What is "the big stage"? If it's the big finals he played, then he sure failed to score, and even played bad, in all 4 big finals. Four matches is not too little to make a judgement, so it's indeed hard to argue when someone says that Higuain failed (or call it choke) in the biggest 4 matches of his career.
Sure, those 4 failures could also be a coincidence and might not guarantee the choker tag. Messi, for example, also lost and failed to score or do anything in 3 of Higuain's 4 finals and he also didn't score in any of the last 4 big finals he played. But Messi has something to show from the big finals he played in 2009 and 2011 and he's not getting the choker tag.
If not just the finals, then what does "the big stage" consists of? Higuain won us the semifinals in CL this year by scoring that brace in Monaco. He also scored a brace in Copa America's semifinals. Four goals in five semifinal matches on the big stage. He's not a semifinal choker then?
Are the quarterfinals of the big tournaments "the big stage"? He won the quarterfinals for Argentina in the last world cup, by beating Belgium 1:0 with his goal. He also scored 2 goals in the 2 Copa America quarterfinal matches he played.
What else is a big stage? He didn't score tons of goals in the CL? Why would a match against, say, Molme in the group stages count for more than a Coppa Italia semifinal against Napoli where he scores 3 goals, or when he wins you the matches against Roma and Napoli in serie A?
You have the finals, and that's a valid argument, although, as with the Messi case in his last 4 finals, it can be argued in a way. It's mostly, or almost exclusively, Higuain's price tag that makes him the scapegoat for the Juve fans.
Lucky for Buffon that we bought him long time ago and his price tag is forgotten. 7 conceded goals in the last 2 CL finals, 4 conceded goals in the last Euro final, and being beaten by Dida in the penalty shootout of the 2003 final would call for some juicy tags.