DNA evidence can prove that a person was at a given location.

Absolutely crucially, that is not the case, Joe. It proves their DNA was at the crime, not that they were. For example, here's a bit about the current state of DNA testing:

=======
One area of confusion is the difference between touch DNA and Low Copy Number (LCN) DNA. With LCN DNA, forensic scientists are able to analyse a very tiny sample of DNA, with anywhere from five to twenty cells.

However, a touch DNA sample will be analysed in much the same manner as a sample from blood or another common type of sample. It is also generally well recognised in a criminal investigation that goes to court proceedings. Commonly, PCR analysis is used to process a touch DNA sample.


Pinpointing a Suspect
So long as a form of contact occurs, there is virtually always an exchange of some kind. Assuming that during a crime, the person committing the crime transfers a reasonable amount of skin cells on some object at the scene of the crime – and if the item is identified and collected rapidly after the crime – then DNA analysis can yield information about the criminal.

=======

So if you have touched the victim, there's some chance your DNA will be found on them. Perhaps you both needed to get to bar or through a turnstile and jostled against each other. Maybe the victim left a party and gave several people a farewell kiss; their DNA will be present. I'm sure you can think of others. These are the sort of things that the victim may well do with dozens of strangers or near-strangers every day, and they illustrate that having someone's DNA at a crime scene is not quite as strong evidence as it appears at first sight.