Here is the pathetic response I got from HMRC when I asked them if a US Government pension is taxed in the UK when paid to a UK resident who either a US citizen or neither a US or UK citizen. I specifically asked about the saving clause and it isn't even mentioned.
Dear Sir,
Thank you for contacting the HMRC Residence Team.
You have not supplied HMRC with sufficient information to verify your identity, so we are only able to give you general advice and nothing specific to your personal circumstances.
I have attached a hyperlink to the tax treaty in force between the United Kingdom and United States of America. Article 19 does indeed refer to Government Pensions:
https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/411900/usa-consolidated.pdf
I can confirm that full relief can only be given on Government Pensions if you are a National and Resident of one state, receiving a pension from the other state.
So my tentative conclusion is that HMRC doesn't apply the saving clause as it's in there because of US CBT. A straight reading of the treaty produces a result that agrees with how HMRC currently taxes US Government pensions paid to US citizens resident in the UK...ie it does not tax them. Also I know of situations where a UK Government pension paid to a US/UK dual citizen resident in the UK is also not taxed by HMRC.
