UK tax on US state pension

If a US citizen resident in the UK receives a state pension from the US, I understand from the US-UK tax treaty Articles 17(1a) and 17(3) that this is taxable only in the UK. However, Article 17(1b) states that "...the amount of any such pension or remuneration paid from a pension scheme established in the other Contracting State (in this case the US) that would be exempt from taxation in that other State (the US) if the beneficial owner were a resident thereof (the US) shall be exempt from taxation in the first-mentioned State (the UK)". In the US there is no tax on state pensions if the individual's total income is less than $25,000. So does this mean that if the individual concerned has income less than $25,000 so the US state pension would be tax exempt in the US, then it is also tax-exempt in the UK? if not, where is the error in my interpretation of the treaty?

Hi,
This is a taxable pension, that some people can receive tax free. This means that it is taxable in the UK.  
The UK state pension is a taxable pension, but some people do not earn enough to pay tax on it. It still remains a taxable pension. The US pension is no different.
Thank you.