That is a poor excuse - the thermal grease should be as THIN as possible to get the maximum transfer of heat. With a flat ceramic chip and smooth heatsink it is only required to fill the minor imperfections in the two surfaces.
I agree absolutely; however, I've also heard the "grease not thick enough" excuse when what was really meant was that the grease was simply the wrong stuff. I've no idea what's used in the modems, but some years ago I came across CPU failures in high-end servers due to overheating arising from grease issues. The spec of the grease had to be something containing heavy metals for greater thermal conductivity.
Unpleasant smells - not necessarily the usual smell of burning - were a common symptom.
Also, I think silk screen application helped to eliminate the erroneous "slap plenty on" mentality.