This is an interesting question.  Technically, there is not anything wrong with this. But should we ask if the violates the intention of the Federal Acquisition Regulations System including FAR Guiding Principles (see FAR 1.102) and transparency.  That's a worthy debate.  

That said, you are not splitting requirements to stay below a threshold.  I think it is how you might ask the question to the contractor, tone could be important.  A common practice would be to tell the contractor what your predicament is and give them the opportunity to "sharpen their pencil a little more".  How do we (you) know that the vendor's confirmation really is the lowest price they'd be willing to accept.  If it really is their lowest offer, they should confirm and then you will have your answer and go through the process of putting it on contract.  Ask your self this, if the vendor knew they had competition, would that have been their lowest price?

Context is important here!!!  I can't overstate that enough.  If this is a one time incident and you are not being heavy handed (or threatening in any way) with the vendor... I see nothing wrong with trying to negotiate a lower price one more time.