This has always bothered me because I grew up understanding the correct phrase to be "the proof of the pudding is in the eating" and assumed that the shorter form arose because of people who simply didn't know what it really meant.
So I googled it and it turns out that the short form, "the proof is in the pudding," has been around since the 1920's (https://en.wiktionary.org/wiki/the_proof_of_the_pudding_is_i...). So, it's got some legs! I still don't think the short form makes any sense, but at least it's not a recent phenomenon caused by clueless hipsters :-)
For example: "Well, that's the exception that proves the rule!"
There are a number of ways to make that make sense, such as the use of "prove" to mean "test", as in "proving grounds", so that's the exception which tests the rule, or, alternatively, the fact it is an exception is proof the rule exists in the first place. Both sensical interpretations.
Of course, it isn't used like that. It's used more like this:
A: "Women can't program!"
B: "Wrong. Look at Grace Hopper, to begin with."
A: "Well, that's the exception that proves the rule! Women can't program."
B: facepalm