All the certificate says is the guy was nominated. It doesn’t say he met the Constitutional requirements to hold the office.
This is where there are problems with the laws. I examined the Virginia code, and it works the same as in all the states where voters are concerned about this: the parties are responsible for the eligibility of their candidates; however, the state election officials are responsible for upholding election laws (notice I did not say enforcement) and, I believe, the Constitution. If the eligibility is a problem, then the party at fault is the DNC. It’s possible that by not putting forth a legitimate candidate, if that turns out to be the case, the DNC would have restricted the first amendment rights of the people of each state. I am not a constitutional lawyer and I don’t play one on tv, though.