A few observations (I am both a Chartered Tax Adviser in the UK and an Enrolled Agent in the US).
1. The remittance basis rarely, very rarely saves any tax at all for a US citizen. Under Article 24 of the Treaty, the US gives credit for UK tax paid.
2. Separately, you are relying on Article 19(2). Any such claim would naturally only be possible if made within a UK self-assessment tax return. This would only be possible if the individual was not a British citizen - and - the pension is a government pension. Whilst there is a strong argument that this a reasonable position, HMRC say here
https://www.gov.uk/hmrc-internal-manuals/international-manual/intm343030 this: "The UK takes a restrictive view of what employments properly fall within Article 19.Generally, relief from UK tax will not be available where individuals are directly employed (whatever their job) in central, regional or local government service. Therefore, civil servants directly employed in central government, those who are directly employed in local or regional government, and members of the armed forces are clearly within the scope of the Article. By contrast, employment in nationalised industries is outside the Article. That is because the services (the work done) was not rendered to the ”State” as such. Those employed in privatised concerns are clearly outside the Article.
In between these extremes it may be much less clear how the wording applies. There may be a blurring of distinctions between public and private sector where employment is with an agency, board or other statutory body, especially where organisations have been privatised or decentralised. Also, structural reorganisations may make it hard to determine which entity is making a payment."
