Flight Instructor back taxiing at a non-towered airport reported they had to taxi off the runway to avoid another aircraft which entered the runway and departed.

Narrative

I was practicing successive landing at Newport State Airport to Runway 34 with a student. This was the favored-wind runway and there is no taxiway to UUU-34. Because of the length of the runway (2623' x 75') we were doing successive landings with back-taxi rather than touch-and-go's or stop-and-go's.After we had landed the Nth time; and passed the taxi stub mid-field on our roll-out; another aircraft came on the CTAF and announced that he was taking the same Runway 34 for departure. I announced that we are still on the runway and have not completed our operation; that what he was doing is not legal. He fired back 'thats ok; I'm ____ (unintelligible).' The other aircraft then taxied back for departure to Runway 34 before we had even made our 180 deg turn to back taxi with the intention of departing again closed-traffic. Hence; we were forced off the runway. We then exited the runway; waited for the other aircraft to depart; then re-entered the runway for another departure.I looked into the regulations and advisory circulars after the fact; and apparently there is no federal regulation against another aircraft taking the active runway while another aircraft is still on it; other than 91.13 'careless or reckless operation.' But it seems common sense not to enter an active runway while another aircraft is still on the runway completing an operation; unless the other aircraft is in agreement. 14cfr91.113 states that the landing aircraft has the right of way over other aircraft in the air and on the ground. And one could argue about when exactly does the 'landing operation' cease and the 'taxi operation' begin in this situation of successive landings and taxi-backs. The fact is; if the other aircraft would have coordinated with us and said something like 'hey; I have an IFR release; do you mind if I sneak out'; I would have said 'sure no problem; let me get off the runway'. But the fact that the other aircraft essentially forced us off the runway and stated that is OK on the CTAF; that is not really cool. I think the FAA should take a hard look at uncontrolled airport operations. The fact that there is no back-taxi at UUU-34 and other airports further contributes to the danger and vigilance required. The recent FAA Advisory 90-66C addressing Non-Towered Airport Operations is a bit pedestrian and dull; and does not address this critical issue of taking an active runway while there is another aircraft still on the runway.