Definitely would have gotten the supplier to overnight a replacement. The thing about warped moulding is that it IS possible to join up nice and square but the key is CUTTING it nice and square (which entails some force at the chopper fence to hold it flat and straight while chopping) then forcing it to join, glue and set overnight in a vise. (So yep, your supplier's chopping person likely noticed it...) No guarantees it will hold, but like you, I myself would have explained the situation to the customer, made it work for whatever function they needed it for, then replaced it at the earliest possible moment after. Most people will understand, and in this instance, should not reflect negatively on you because you didn't cut the frame....
One tip to try if you are going to force a frame to join up in a vise is if you have a gap on the inside or outside of the mitre, loosen the vise and put a small shim or piece of folded-up paper (I use a couple of pinner nails broken off the stick of nails for bad gaps) between the inner rabbet of the frame and one end or the other of the inner vise jaw (the one that does not move; not sure that's the right term); which end of the jaw you place it on will depend on where your gap is. Envision which way the moulding needs to bend to close the gap and put the shim where it would gap away from the jaw on the inside. In other words if the miter gap is on the inside corner of the miter, the spacer/shim (no more than 1/16" thick depending on size of gap) needs to go at the inside end next to the inner corner of the vise; if it is on the outside corner of the miter, it needs to go on the outer end of the jaw away from the corner.
This will force the miter surfaces together more effectively so they are in contact the entire width of the miter, so the glue will hold the surfaces together. BUT, a good frame in that situation is going to depend on it being held square when cutin the first place and sometimes it is just too much warp or bow. Some moulding is just too twisted or warped to make this work, and you should be entitled to a replacement.
Of course there are limitations to how much force glue and nails can hold...and like Rick states, a short frame in a wide profile has very little give to it.
And I will chime in with the rest, whoa, that's a LOT of distance OFF for such a little frame....so either bad miter angles or major bowing in one or more legs. If you sight down the legs by holding the end up to your eye level and looking down its length, you can usually see right away where the problem is.