It all seems to come down to a semantic quibble. The US clearly isn’t trying to tax the UK State Pension when received by a UK resident, any more than HMRC is trying to tax US Social Security when received by a US resident. It doesn’t really matter whether a UK pensioner in the UK reports his State Pension to the IRS as “taxable” or not, since it won’t, in fact, get taxed by the US.
The UK doesn’t care, the US doesn’t care. Report it, and get the tax credits, or exclude it and file a simpler return or (if below the threshold) no return.
Or it can be taken up with the horses’ mouths, by writing to the Competent Authority.
HMRC’s view has no legal standing in the United States.
And the IRS’s view has no legal standing in the UK, where we happen to be and where the pension under discussion gets paid.
But the UK Government, and the US Government, have reached agreement as to who will tax and who will concede, in order to try to avoid double-taxation (as defined by the treaty); so the views of their respective tax agencies, in their rôle as Competent Authorities, do carry weight via the Mutual Agreement Procedures.
Presumably, if it turned out that the IRS disagreed with HMRC’s expressed position (that social security is taxable exclusively in the residence country), discussion would ensue and a new common position would be agreed. Mutual Agreement, as they say.
(Though it seems to me rather more likely that the two countries have actually already agreed that social security is taxable exclusively in the country of residence, given that that’s what both countries do actually do.)