This manager said a lot of stuff without actually saying anything!
He clearly does not want to get involved, but to leave the episode unchallenged could lead to a dangerous previous imo.
If the bowlers have convinced themselves that cycling is not allowed in the park, then maybe they are saying it to other cyclists too, that could believe this, avoiding the park as a route.
Maybe, Sara, you could lobby for a few signs that clearly state cycling is allowed, get the local councilor involved, or local cycling activist groups.