Pure OO, except for the script invoking the controller PM.

Not really understanding how this relates to my comment. In a "Pure OO" module, you could still have a spurious lonely shift.

Since @ARGV is global, it is available to all PMs, but better design dictates not referencing it within deeper OO code.

Yep, certainly! So what?

One PM has a filehandle read, but can this be shifting it just by being included in a "use"?

No, it can't. I suspect it's something else. Still hard to say without seeing any code. Of course the actual one may be too large to be posted here. You should try to trim it down to a bare minimum still exhibiting the problem and while doing so you may even find out yourself at which point in the actual code the shift occurs.