No. As already suggested, your observations are very difficult to reconcile. Here is why:
From your ATS (Automatic Transfer Switch) onward to main 120 VAC breaker box and all circuits supplied by it (including the converter) there is just ONE supply (one hot, one neutral and one ground with 30 amp, two hots, one neutral and one ground with 50 amp).
So, if shore power powers the converter AND other 120 VAC circuits work with generator (roof A/C, microwave, 120 VAC outlets, etc) the converter should work as well since the exact same wires run from ATS all the way to converter.