With the resonant frequencies of input filters, yeah, most filters have them, but perhaps the remainder of the DUT is fairly tolerant to noise at frequencies at this range, perhaps there's filtering going on elsewhere in the system which rejects it better. Good design in the rest of the system is one way to get around it, as it cascading filters to improve rejection at either filters' resonances.
I wouldn't necessarily word it around testing the effectiveness of the input filter, it's more about testing the response of the DUT. If you consider that the DUT may receive and "detect" the incident signal/wave, perhaps on an analogue input with some nonlinearity, the modulation can help reveal its presence since the "error" would appear as a 1kHz sinewave. I believe the modulation is supposed to make the test signal more representative of an AM modulated radio signal.
The modulation does present three frequencies (in comparison with an unmodulated carrier containing only one frequency), at f_carrier, f_carrier+f_modulation and f_carrier-f_modulation, but with a separation of 1kHz, there aren't many properties of an input filter that would be particularly revealed in that case compared with a non-modulated carrier. It can be a more intensive test of the DUT itself, as a system that would be able to reject a DC offset caused by "detecting" a continuous-wave incident field/signal, now has to contend with the 1kHz it will be demodulated as... so its not really anything specific to do with filter resonances, but indirectly, yes, they would let through more of the incident signal making an existing problem worse.