Re: One thing that apparently happened after this story was posted
I suppose by drilling a somewhat larger via into one of the internal layers you should be able to hide a chip in the cavity it creates without any bulges whatsoever. Yes, it would be noticeable if you examine the board structure carefully (ie. knowing what you're looking for, by x-ray / transparency) but probably not on a cursory looking-at-the-external-layer-only check.
And I'm not sure such a method would give away anything extra - even if your chip is on the outside, mounted on the surface as any other chip, it would be clear from the PCB layout / trace / footprint modifications necessary to mount it that it was a job done at the factory, while such an extra component would be much easier to notice than an internal chip even on a less thorough check of the PCB.
The only way to plausibly deny the source of the modifications would be to bodge in the extra chip rework-style (possibly even requiring extra patch wiring) but that would stick out like a sore thumb at any kind of glance to anyone opening the case - and even that would merely shift the blame away from the factories themselves, still leaving China as the only logical suspect, unless someone tried blaming the NSA & co.