It's certainly true that a "proof of concept" will not necessarily prove the concept. The test may fail. But that fact is hardly unique to this particular use of the word "proof". If you say, "I am looking for proof that the Polynesians discovered America", you may or may not find such proof. Etc etc.
When a proof of concept test is completed, if it was successful the concept is "proven" or "proved". If the proof of concept test failed, then the idea is either "disproven" -- we proved that it doesn't work -- or "unproven" -- the results were not adequate to say it whether it will work or not.
"Proof" as a verb is generally understood to refer to examination of text for errors, as in "The editor proofed the manuscript." I don't think I've ever heard someone say, "The engineer proofed the airplane's wings" or "The accountants proofed the tax software". Certainly not, "The physicist proofed his cold fusion theory." The verb "proof" has very little to do with the noun "proof".