I had a head on with a lycra clad trail warrior last year on the C&O canal towpath, they had pulled out to overtake the other members of their group despite the lead rider shouting that I was coming, no harm done as I landed in some bushes but they were a little cut up, still not as bad as the broken ribs I sustained a month later when I was rear ended by a car, there is some danger but I would say it is minimal and don't let it put you off riding bike paths, they are safer than roads.