Very much the instructors fault.
There are established intercept signals that are in the regulations, and the instructor should have been aware of them. These com-out signals are designed to deal with NORDO situations. (And not knowing where you are and where you are going and not being able to hear/transmit on the radio--allegedly--then the instructor should have used his certified judgment and followed intercept procedures.
Very rare to find a private pilot, especially two inexperienced ones, who are familiar with military intercept proceedures. They DID try to communicate on 121.5 & another freq, to no avail (not their fault). Sure, they screwed up, but it should not have been the big deal it became.