I have a travel FA kit in the boot of my car with all the usual stuff but the point is (as alluded to by others), unless you are trained and indeed certified, while most people would be happy to accept basic assistance the site should have nominated, trained and most importantly, insured First Aiders on site.
If you render aid and something does go wrong then not only are you potentially opening the site up to a liability claim, you also open yourself to one. I know we don't live in quite the litigious society that exists in the US but it DOES happen.