They may have objected to your assertion in the first paragraph ("....the ratio between the repetition frequency of the pulses and the frequency of the sinusoidal signal must be a fixed known value.")
Admittedly I'm not well-informed on this topic at all, but I haven't run across that exact requirement. You need to know the pulse rep rate, which in practice may just be a matter of triggering the laser from a sufficiently-stable source rather than having to measure it separately -- and you need some way to get a carrier beatnote from a pair of lines, where the F-2F technique is a common approach -- but do you really need a priori knowledge of the PRF:carrier frequency ratio in order to make the whole thing work?
Admittedly I'm not well-informed on this topic at all, but I haven't run across that exact requirement. You need to know the pulse rep rate, which in practice may just be a matter of triggering the laser from a sufficiently-stable source rather than having to measure it separately -- and you need some way to get a carrier beatnote from a pair of lines, where the F-2F technique is a common approach -- but do you really need a priori knowledge of the PRF:carrier frequency ratio in order to make the whole thing work?