Please tell me where it says that a CFI must have flown on all of the students flights? More to the point how exactly would you expect that to work if a student changes instructors?
Well you could look at it like this....every flight done with you, in the eyes of the FAA, is a flight with just "someone", but NOT a CFI. Therefor the time, in the FAA eyes, does not count for jack with regards to instruction. So then to have an FAA CFI "sign off" this time is sailing very close to the wind - (s)he is effectively lying - stating that the flight was an instructional flight, but in actual fact there was no instructor in the aircraft providing the instruction (in the eyes of the FAA)....
I have come across schools like this before, but the difference being that all the FI's were FAA FI's, with "knowledge of JAR"....rather than they way you are doing it...