Yes as you pointed out the APU has got a check valve on all versions.
Quote from Operations Manual 2.20.2:
"With both the APU and engine bleed valve open, the engines operating at idle thrust, there is a possibility of APU bleed air backpressuring the 9th stage modulating and shutoff valve. This would cause the 9th stage valve to close."
From the above it is clear that what Boeing fears is APU pressure going into the engine, not the opposite.
That's why it seems that increasing power would help preventing this problem.
Can anybody explain this to me?
