No, that is not true.I don’t know about the whole longevity claim of a server chip over a HEDT part. Properly cooled a HEDT chip should last just as long as a server chip.
The longevity of a processor core depends mainly on 2 variables: the temperature (on which the degradation of the insulator layers depends) and the electrical current consumed by the core (on which the degradation of the conductor traces depends).
A core in a "server" CPU, e.g. Xeon Scalable or Epyc, is operated at a much lower maximum power than a core in a "workstation" CPU, e.g. Xeon W or Xeon E or Threadripper or Ryzen 9. That means it is also operated at a much lower maximum electrical current per core.
This is the reason for a longer lifetime when the CPU runs all the time at high load, even if you use a perfect cooler. With a bad cooler, obviously the lifetime will be even shorter.
Nevertheless, if you use a "workstation" CPU and you either underclock it or it stays most of the time idle (with power state management being active, e.g. with the "powersave" governor active in Linux, to reduce the clock frequency when idle), then of course you can achieve a longer lifetime than a "server" CPU that is 100% busy.
So the "workstation" CPU will have a shorter lifetime only when it is busy all the time, as it is normal for a real server application.