I am reading 61.75 and it describes a piggyback license
The term piggyback of "based-on" is commonly used. However, it has no particular meaning.
A part 61.75 licence is a fully valid FAA certificate the validity of which is dependant on an associated foreign licence. This does not diminish its standing as a licence in its own right - as evidenced by the requirement for holders to submit to BFRs, regardless of the validity of the associated licence.
This is entirely different from "rendering a foreign licence valid" as described by Bookworm.
This process typically involves the issue of a letter of validity to be carried with the original licence.
A fine point perhaps, but so is much of aviation process.
2D