It is a very odd scenario where we are all told to be on the look out for scam callers - be it banks, airlines, energy companies, etc - but there seems to be a stalemate around how the caller proves they are legit.

Maybe a code word should be used by these companies, that is agreed with you. If they don't say the word/phrase after introducing themselves then they're not who they say they are? I wonder how much time and effort that might take. Much fun could be had by setting your BA phrase to whatever your bone of contention is about their service