It isn't so much the apu air back pressuring the engine as it is that the apu air will close the high pressure shut off valve and fool the high pressure regulator into thinking there's adequate pressure to the system. The NG PRSOV and HPSOV are commanded closed in a start sequence to prevent back pressure in the engines. Once the engines are running there's little danger from the apu air but there are other problems.
If the engine(s) are powered up with the apu providing air to the same duct system there's the possibility of the HPSOV "popping" open with a resultant "water hammer" effect causing a duct rupture.
Here's a link to a page and schematic that should help you make sense of the engineer's dream:
http://www.b737.org.uk/pneumatics.htm