The second visit should be done by your vet or another independant vet and the extent of the exam should reflect the purchase price of the horse. For instance a pleasure horse does not need x-rays, a show or breed horse will.
A few years ago I lost a very expensive investment stallion to "wobblers" so make sure the vet can do a proper neuro exam.
The 10 day trial makes it very nice as you can discover many things about a horse during that period. Perhaps it is something you can negotiate with a seller there in the US.