Weight distribution hitch BARELY won't fit into receiver

Have you thought about running to the nearest Toyota dealer and checking a different 4 Runner?

You might have dodged a bullet here- the only 4Runners that had frame-mounted receivers rated for use for W/D were the V8's. Since they didn't put those out in 2012, I'm assuming you have the V6- factory hitch on that model is NOT for W/D. It should say so right on the receiver, and probably also in your owner's manual. Reason is method of mounting- the OEM's on the V6's are attached to the rear cross member only, whereas the W/D receiver on the V8 models mounted directly to the frame rails. This in order to deal with the rotational stress torque imposed by W/d systems.

That said:

It does seem unlikely that a (2"?) hitch bar itself wouldn't slide into the receiver for that reason unless Toyota actually built in some feature to prevent their use. If W/D's shank is longer, for example, than a standard weight-bearing ballmount, the smallest of curvatures in the receiver tube would do just what you describe- prevent full insertion.