We have always had at least the vet, barn manager, owner, and owners family (sometimes students as well) in the stall after the birth. It is usually around 5 or fewer people in the stall. That said, our mares are very, very good about having people around the babies. We also tend to encourage others (who are horse experienced), particularly at boarding stables to pet/handle/lead the foals. The foals from these sort of situations tend to be very easy going, easy to work with and people oriented. Keep in mind that horses are precocious and are able to run within 2 hours of birth. So, they are basically born ready to learn. For our horses, humans are part of their every day life and a key element to them being successful in life. It makes it easier for them as young horses to be broken to harness if they are already used to people touching them everywhere, being everywhere. They don't know any other life other than people being around.
I think its odd that they did not allow the vet or share the vet report.