The lender is acting at the behest of the government when they follow KYC regulations. The 4th amendment specifically protects against this sort of search of your 'papers'. KYC is a search. It's a government requirement to have your papers searched-- akin to a policeman asking to see your papers before you get the loan. That's a search.
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>If you are stopped by the cops and they ask if they can search your car and you say “yes” then the search is valid. You are allowed to say “no”. They can force the search under certain circumstances.
OK I say no and the policeman has no probable cause to search. What happens next? Am I allowed to continue my elective activity of going down the street, or can the policeman pull out a gun and tell me I'm going to jail if I continue to electively head towards my destination? I think you know the answer -- when I decline the search it has no effect on my elective ability to complete my task of continuing on the roadway. Returning to the loan, the analogy here is I would be allowed to proceed even after declining KYC search.
>You are allowed to say “no”.
Going back to your example of the cops stopping you, when I say no I'm eventually allowed to continue on my way. I'm not turned around and stopped from completing my elective activity. By your logic government could just pass a law that whenever you elect to leave your house, your constitutional rights are waved -- that's just ludicrous and defies reason for having them in the first place. You're not allowed to say 'no' to following the KYC search and keep on going -- It's a forcible search.