Precisely.

According to this link, "BN(O) citizens do not have the right of abode in the UK" (emphasis added).

Granted, BNO does provide a fast-track to UK permanent residence and eventually full UK citizenship, but this requires an application process as opposed to being an entitlement.

I am not an expert in this but it seems to me that the word "British" in BNO is a bit misleading. The "overseas" part of the BNO is what matters, and this is what precludes the holder from having the unrestricted right to live in the UK.

In short, entering the UK as a BNO seems entitle the holder to slightly more privileges when compared to entering as a US Citizen, although the BNO citizen still falls short of benefiting from the full privileges of UK citizenship.

Additional information regarding BNO is available here:

https://www.gov.uk/types-of-british-...ional-overseas

Note the following: "[You] are subject to immigration controls and do not have the automatic right to live or work in the UK."