Grit, don't be to hard on the previous owner.:). He may have thought the tanks were clean BUT:
Many times, "stuff" gets left behind when dumping, even with using the tank rinse. This is usually in the corners of the tank or just on either side of the dump valve location in the lowest part of the tank.
I have found the best way to get this stuff out, is to use a "down thru the toilet" wand to blast the stuff out. It usually takes quite a long time with spraying down there to get the job done. I used to do it at least once per season right at the end before we returned home from our snowbird site and still do the same thing today after our last camping weekend of the season. We have a built in tank rinser that I use every dump but the stuff still seems to accumulate in the locations mentioned.
I used a wand similar to
this one except mine had three holes in the end for the water to come out of. I like this one better as it should be easier to "aim" at the poo piles and probably give a stronger blast of water.
The first time I used this it took quite a while to stop the pieces from coming out - probably old dried "stuff" being broken up by the water blast. Subsequent years it did not take nearly as long.
Hope you find the above helpful and not too gross! :B
Barney