The guy has it just backassward!!
The recommendation is to use a flush before changing to synthetic, especially in higher mileage cars. If you don't, the synthetic will clean the same way, just taking longer. And, in the process, it is possible (in highly sludged cars) to plug up the filter with gunk--and have higher oil consumption as a result.
If you've already changed (sounds like you have) and didn't use the flush, don't be concerned. Just watch for any sudden increase in oil consumption. If you do get that, change the oil filter and top off. Otherwise, plan to change the first batch of synthetic after 3-4,000 miles.