In SQL Server, is parallelism per operator, or something else?

I work with a really old DBA who says a lot of weird stuff. Dude has an O'Reilly book that only has an amoeba on the cover. At lunch we were talking about parallelism, because our new server has 24 cores. He says that in a parallel plan, every operator gets DOP threads. So if you have MAXDOP 8 and your query has 4 parallel operators it'll use 32 threads at once. That doesn't seem right because you'd run out of threads really fast. I also read that it might just be 8 for the whole query, which seems like too few. Why Do I see more threads per SPID in sysprocesses than MAXDOP? Are either of them right?