All this assumes that the jet concerned is of a higher vortex wake category then a C152, if that was the case, then the atco concerned was wrong for the reasons already given.
However, there are a number of "jets" which are in the smae vortex wake band as your aircraft, consequently, the departure separation would not apply, (even if the atco gave you misleading information).
When I learnt to fly, my instructor was fairly picky about me assessing whether I could accept an immediate departure behind the preceeding aircraft, and also looking up the approach prior to departure to find out where the next aircraft to land actually was.
If in doubt, stay where you are and remain comfortable.