It is true for the H1B holders with the visas under 6 years. However there is a whole class of H1Bs who had been in status for longer. They manage to extend their status beyond 6 years based on approved I-140 and the fact that they cannot apply for a Green Card because of the country limit. For these people the H1B is the only available legal status and it entirely depends on the I-140, which belongs to the employer.

Theoretically, nothing prevents them from changing jobs just like with a <6 y.o. H1B. Also, theoretically, nothing prevents the old employer from recalling the I-140. In such a case there are, probably, ways to still retain legal status but they are far more complicated than filing for a new H1B.