If it were a katana, so what? Is it illegal to carry one around? It's probably against school rules like guns are, but I doubt the SWAT team would be called just because a guy had a gun, especially if it wasn't a college campus.
Do I think he has a right to have the umbrella in public? Absolutely. Do I think he should exercise a bit more discretion considering the circumstances? Yes. But there was some serious overreacting here, either by the person who reported it, or the police.
edit: My university has recently had several occurrences of 'alleged' gun sightings (that turned out to be cell phones), and each time the police has responded with one or two armed officers to investigate the situation. A measured, but conservative response.
The look on a neighbor's face when you've got a TRG-42 slung over your shoulder in the elevator is priceless...