They are correct in that the strut caps, what some might call the "top hat" should have been replaced if they were in bad shape. Given a 2011 Xterra driven for several years, safe bet they were in bad shape....
The metal part is irrelevant, I replaced mine because it was a cheap part and it's always better to assemble new parts, but the main parts to replace are the 3 bushings, one big one the coil sets on, and 2 small ones that sandwich the metal top hat.
That does not rule out them screwing up. They might have missed the bushing under the metal hat. We can't see if they put that on or not until it's off. It could simply have rode on the old bushings a while and it gave up like they suggest though, hard to say without looking at it.
It is good practice and would have been worth your while to replace all the rubber parts while it was out. You depended on your mechanic to do the job and if they were good at their job, they would have asked you to do this or included it as part of the job. This is why I don't have much respect for most auto mechanics...
This shows the proper stack, it's a but complex to interpret but simple once you have it in hand:
It can change somewhat with aftermarket setups. Old Man Emu simplified and improved the upper shock mounting dramatically.
This is the stock setup that came off my X: