Yes, it is anomalous, but in UK thinking, so is the situation of holding both a Royal warrant and a Royal commission. The US, not having a "Royal", do not encounter this apparent disparity.
I presume that you mean not being allowed to stay in an officers' mess; that's probably because of a lack of knowledge/information in UK military circles about the status of CWOs (certainly the RAF not knowing about anyone's army, let alone the US
, and the aforementioned anomaly).
Mister B