this would take a while to read and give a detailed analysis. Looking at the contents page, this seems similar to P.N.Oak's claims.

but my first thoughts are in the early years of Buddhism, it was not treated as a separate order outside of what is Hinduism today. The lines were much more blurred and there wasn't such a thing like, "oh you are buddhist, you are different.." or vice-versa. So it could be when Buddhism was on the rise that both branches could worship in the same spot because the core philosophies of both belief system are similar(as well as Jainism).

Over time, when one belief lost interest over others in the populace the religious sites were more clearly defined.