Not only is the 3rd party "right", he may also be (knowingly or unknowingly) revealing "trade secrets" from other manufacturers he has witnessed prior to your operation.
Yes, API is silent on this issue. Some manufacturers have practices in place that prevent machining in this area. Unless the purchase specification forbids this, however, the 3rd party should remain silent, even though he may believe it is not good practice. The 3rd party's function is to make sure the manufacture is in accordance with the prescribed specifications, not to make all manufacturers obey what he believes is "best practice". The particular 3rd party could land himself (and his employer) in considerable legal trouble if the right (or wrong) people learn the details of this.
In my opinion, you should tell the 3rd party to bugger-off. It is not his place to tell you how to run your manufacturing; only to make sure you are conforming to the purchase order requirements. If the 3rd party decides to escalate the issue, the more likely the revelation of "trade secrets" will come out, which is where the 3rd party firm will back down and pretend nothing ever happened (if they are smart).
The actual effect this has on the life of the pipe is little to none. While, in theory there may be a difference, in practice the effects of wear of the pipe in service will out-weigh this small effect as to make it inconsequential (ever see what drill pipe slips do to the OD of the pipe? And he is worried about flow lines on the ID? This is so obvious that he is trying to impose another manufacturer's in-house requirements on you that I would be surprised if it is even mentioned on Monday morning).
Ask him what other manufacturers he has been a 3rd party on. Document it. Then tell him that if he wants to make anything of it, you will tell his boss that you will contact these other manufacturers and tell them what you are asking of them. If you do that, you will see the faster "crawfishing" than they've ever seen in southern Louisiana.
rp