Dogs are not stupid. . . . although you shouldn't over exercise a pup, they are usually very good at self regulating. Things I wouldn't do with a young pup would be sprinting, or jumping etc, as it can put unnecessary pressure upon their bones and joints.
However, my pups are out all of the time, following me around, (albeit at a slow, stop / start pace), but other times, they just refuse to and have nap or want to be carried. I let them self regulate, unless I see an obvious problem.
Ive had a range of breeds, all of which had led very long, very active, working lives.
As for the vets advice. . . . .if I had a 5 month old pup and it only got out and about for two half our slots a day, I would consider it under stimulated and under exercise. They don't need to be running marathons, but they also won't learn anything sat in a crate!!!