I am currently studying Path Integrals and was unable to resolve the following problem. In the famous book on Path Integrals written by Feynman and Hibbs it says:

So far we have described quantum-mechanical systems as if we intended to measure only the coordinates of position and time. Indeed, all measurements of quantum mechanical system could be made to reduce eventually to position and time measurements [...]. Because of this a probability theory formulated in terms of of position measurements is complete enough to describe all phenomena.

To me this seems to be a highly non trivial statement (is it even true?) and I was unable to find any satisfying elaboration on this in the literature.

I would be thankful for any answer to resolve this question and any reference to the literature!