Those tests are pretty accurate. With your mares estrone sulfate level at 4.8ng/ml she would have to be Very close to foaling for your vet to be wrong, it's known those levels will drop just prior to foaling so he may be. Looking at the photos I wouldn't rely on the vets prognosis just yet. Yes it is correct that level would be a negative, but the Vet was hands on with your mare so giving you that result after examining her doesn't make sense looking at these photos. I've had many mares look just like this right before foaling but I also have to add I've had open broodmares look the same.
May I ask were you given breeding dates? Also you referred to her as a filly is this her first foal?