I'm afraid this is absolutely not the case for UK passports in the US, which must have at least 6 months' validity remaining to ensure continued entry to the US, even for those like myself with a permanent resident card.
The UK passport agency now regularly add an additional period to the validity of a passport for this very reason. For example, if you renew 7 months early because of the US's 6-month rule, you will receive a new passport valid for 10 years and 7 months, compensating for what you lose by early renewal.
For UK non-immigrants visiting the United States, the UK passport is only required to be valid for the length of the intended stay in the United States not 6 months beyond the intended stay. (UK is a member of the "6 month club") This is by international agreement. If you are a Permanent Resident with a valid LPR card, you are not required to have a valid UK passport at all. All you are required to have is a valid LPR card, valid re-entry permit or valid refugee travel document upon entry depending upon your individual circumstances.
FB
http://www.cbp.gov/linkhandler/cgov/...n_04162008.pdf
http://www.getyouhome.gov/html/lang_eng/eng_sa.html