I would say a mechanism that effectively bypasses the 4th amendment has quite a lot to do with the 4th amendment. The intention behind the rule was not that it was OK to ignore it as long as money changed hands.
While your sentiment is valid it does not apply in this context. There is no activity the NSA performs that would require a warrant. In order for the fourth amendment to be necessary the collecting party must be the government, the possessing party must be inconvenienced or distressed, and the action must result in either involuntary seizure or violate a legally recognized expectation of privacy into public. The NSA only accounts for 1 of the three necessary ingredients.
What this reminds me of is the free speech vs. 1st Amendment doesn't apply to private companies discourse in the sense that the spirit but critically not the letter of the amendment is broken