What claim? My comments are based on spec. You can read about the 4 sub xlr connections from the Masimo video and Audioholics, or read the manual. And on performance, in many reviews SINAD did not always do better, worse on some occasions, and when they did do better, most of the time, the differences ware 2 to a few dB. As for grounding, that is not what it is about, but about noise cancellations inherent in balanced configurations, that could be significant in cases where interconnects are long, but not so much for the typical 2 to 3 meter lengths. Of course on all else being equal basis, xlrs should perform better in terms of measured SINAD. I am just cautioning that they are not always necessary. They also offer 2x the voltage so with some amps it could be an advantage too and I am sure you know that already.
Anthem's are all xlr for their AVPs, not AVR/AVC. The AVR-A1H is an AVR, and it is rare for AVRs to provide 3 or 4 XLRs. The Yamaha flagship offers only 2 XLR outputs.