Although the attitude Richard has going about this is uncalled for, it is this kind of comment that is getting him upset. The argument above, that the downhill will make up for the uphill in most cases, is just plain wrong. You personally may be faster on hilly courses, but it's because you're putting out a good deal more effort all around, not because hilly courses are inherently faster.
Say you go 10 mph up a 1 mile climb, and 30 mph down. You DON'T average 20 mph, because you spend 3 times more time at 10 mph than you do at 30 mph. Your actual average? 15 mph.
If you're going so slow you're almost falling over, you're going to be killing your average speed. Say you do a 5 mile climb at 5 mph. Now if you descend the same way, even if you descended at an infinite speed, you would still have spent an hour climbing, and would average 10 mph. The only way you might be able to make up a bit more is if the descent is much shallower grade and longer than the ascent, but over a lengthy ride these kind of effects will be insignificant.