Well, there is nothing unusual or proprietary about almost all steel or Ti frames but as the saying goes; "the devil is in the details". It's highly unlikely the Chinese company will exactly duplicate the drawings you have and, since the differences are likely to be internal (butting. tapers, etc.) you will never know from outside appearances. Also, the weld quality is an unknown and any warranty claims or disputes about what they provided will be difficult or impossible to enforce. As to the plans not explicitly stating they are copyrighted, I would not want to have to defend that position in court. Those are the practical considerations.
Ethically, I've got a real problem with using the plans you received to shop for a lower price. The provider sent them to you in good faith and expected you to use them to choose one of their frames, not as a negotiating tool.
Yes, buying from a top-of-the-line Ti maker is EXPENSIVE but you get custom quality and fit and a local source to assure that if things aren't right they will be corrected. Do yourself a favor and sleep better.
BTW, I'm not sure which domestic company you are dealing with but consider Lynskey (if it's not already them). They are the founders of Litespeed and have decades of Ti experience as well as reasonable prices. If anything happened to my Litespeed that's where I would go.