(Semantically, “ten minutes' walk” still means ‘a ten-minute walk’ rather than ‘the ten-minute walk’, but your point in reply to shminux was about syntax not semantics anyway.)

The "proof of synonymy" looks like this:

ten minutes' walk = (the walk) of (ten minutes) = a (walk of ten minutes) = a ten-minute walk

...the second "equality" being where semantics is invoked.