Having three hunter pointer retrievers I would agree. It is not safe just to let the dog go off on 4 acres without supervision.
I take mine to a 12 acre field every day for exercise, but I walk round with them and they check in every few minutes or so - it is deer fenced and single gated, but the bottom half is chicken wire so there are occasional gaps due to deer pushing in, so not 100% safe.
Because of that I have them recall whistle trained and if I don't see them for a longer period than I like they are whistled in and given a treat then sent off on a 'goandplay' command.
So I would advise whistle and stop training your dog and doing a strict perimeter check to reassure yourself of it's security, before letting him/her loose on your ground. And only when you are within recall distance.
If really excited a dog will manage to get round/over/through most barriers and coudl cause an accident or damage property/other animals. Your responsibility; your call.