Wow, interesting. Many seem to want to put the pilot(s) at fault for descending below the Arc alt of 10,000'. They were cleared for a RW32 VOR/DME C Approach via the arc. MVA's do not enter the equation. It is quite clear via the approach chart there is no decent blo 10,000' until the intercept. That said, there is no way the controller should be mentioning anything about 7800'. That is very very poor and I would guess it is a local unit procedure that must be addressed and eliminated. I am a long long time controller of which the last 25 years have been in Approach. Fix it.