What no one can EVER prove is that they covered Jesus. People are so gullible. Research money is so available.
I’m not sure I understand your point here but clearly the Shroud was used to cover *someone*. So if someone else in history was covered by a burial shroud why wouldn’t Jesus have been so covered?
Or, if one starts with the assumption that the Shroud is a complete forgery, then one still has to deal with the historical fact that indeed burial shrouds were in quite common use back then. So again the question would be “Why wouldn’t Jesus have been so covered?”
I would think that the burden of proof would lie on the claim “Jesus wasn’t covered by a burial Shroud”; the claim “Jesus was covered in a burial shroud” seems verifiable by historical evidence alone.
The people doing this research usually pay for it themselves. Scientific evidence that is replicable has nothing to do with gullibility.