Oh man.....you had to bring me down. 
Sorry Fred, ....I'd never want to bring you down!
It's a common problem and depends on the definition and context of "state". The statement you are remembering probably was in reference to a UK
State pension.
Services rendered to the "state" are the key.
For State in the terminology of international sovereign countries, and pensions
not awarded for
services rendered but as part of an old age social benefit, the tax treaty reference is Article 17.3. Example: The UK State Pension to which we all contribute through NICs. Pensions awarded by the UK government or the US government for
services rendered to those governments, are covered under Article 19.
For State in an American colloquial sense, pensions from States such as California, Illinois, Iowa, etc., awarded for
services rendered to that State, are covered by Government Service, Article 19 of the treaty. (Local, not national, jurisdictions.)
Local jurisdictions can also include jurisdictions such as, for example, Cook County, Illinois, LA County in California, the City of New York, or the Warwickshire County Council in the UK; or the military, certain publicly funded educational establishments, State and local police, etc.. (Article 19)
So iffffff I read the comment from Nun above correctly......My US Fed Gov pension is taxed only in the US as it currently does. But....iif I were to take UK citizenship as well in a few years like I had been pondering.....it would get taxed in both places. If so.....it would definitely not be to my benefit to get UK citizenship. Jeez.....and here I am trying to quit drinking beer....
The answer is in Article 19, paragraph 2, subparagraph b. The following is from the "Technical Explanation" (page 69), and was written by the US (the UK may not agree).
"Paragraph 2
Paragraph 2 deals with the taxation of pensions paid by, or out of funds created by, one of the States, or a political subdivision or a local authority thereof, to an individual in respect of services rendered to that State or subdivision or authority. Subparagraph (a) provides that such pensions are taxable only in that State. Subparagraph (b) provides an exception under which such pensions are taxable only in the other State if the individual is a resident of, and a national of, that other State."
https://www.treasury.gov/resource-center/tax-policy/treaties/Documents/teus-uk.pdfThe UK will want to tax a US government pension paid to a UK resident UK citizen (national) as required by the treaty. The US agency providing the pension, regardless of the treaty, may still want to inflict withholding of US tax if the individual is also (or remains) a US citizen, even if notified of the treaty position of the individual. In this case, the individual would file a form 1116 to the IRS using the "resourced by treaty" basket to reclaim the withholding for this specific pension from the US. This could be in addition other forms 1116 filed for additional General and Passive income.
