I have an application for a loan that was taken over the internet. It was denied. The applicants checked on the application that they did not wish to furnish the government monitoring information. Obviously the lender could not make a visual observation so if the information was not collected is that a violation?

no. Mail/internet/phone applications do not have to be filled out for GMI if the borrower declines to provide the information.
Some BOLers collect it at the closing table and report it.
Others, myself included, hold to the principal that HMDA is based on the APPLICATION so what you get when the borrower applies is what should be reported, even if you see them later.
Either way is correct per GIR