If you have low income then the larger UK tax free allowance than you get in the US might mean that you have zero UK tax and have to pay tax in the US.
The tax treaty and US and UK domestic laws eliminate double taxation, but you will pay the larger of the tax in either country.
I see it differently.
The purpose of the treaty is to avoid both double taxation and tax evasion. If a particular interpretation of a provision in the treaty appears to result in double taxation for an individual, it's probably just a misinterpretation. Rarely, it might be due to infelicitous wording in the treaty language, or might be an anomalous case. (I say rarely, because it seems likely these treaty-writing legal professionals do know what they're saying, and also seems likely (to me) that any ambiguities and infelicities would have been corrected long ago, probably in proofreading. And anomalies, by definition, are rare.)
If it's an anomalous case or due to ambiguous wording, Article 26 (Mutual Agreement Procedure) applies:
1. Where a person considers that the actions of one or both of the Contracting States result or will result for him in taxation not in accordance with the provisions of this Convention, he may, irrespective of the remedies provided by the domestic law of those States, present his case to the competent authority of the Contracting State of which he is a resident or national. The case must be presented within three years from the first notification of the action resulting in taxation not in accordance with the provisions of this Convention or, if later, within six years from the end of the taxable year or chargeable period in respect of which that taxation is imposed or proposed.
2. The competent authority shall endeavour, if the objection appears to it to be justified and if it is not itself able to arrive at a satisfactory solution, to resolve the case by mutual agreement with the competent authority of the other Contracting State, with a view to the avoidance of taxation which is not in accordance with this Convention. Any agreement reached shall be implemented notwithstanding any time limits or other procedural limitations in the domestic law of the Contracting States, except such limitations as apply for the purposes of giving effect to such an agreement.
3. The competent authorities of the Contracting States shall endeavour to resolve by mutual agreement any difficulties or doubts arising as to the interpretation or application of this Convention. In particular the competent authorities of the Contracting States may agree:
(a) to the same attribution of income, deductions, credits, or allowances of an enterprise of a Contracting State to its permanent establishment situated in the other Contracting State;
(b) to the same allocation of income, deductions, credits, or allowances between persons;
(c) to the same characterization of particular items of income, including the same characterization of income that is assimilated to income from shares by the taxation law of one of the Contracting States and that is treated as a different class of income in the other Contracting State;
(d) to the same characterization of persons;
e) to the same application of source rules with respect to particular items of income;
(f) to a common meaning of a term;
(g) that the conditions for the application of the second sentence of paragraph 5 of Article 7 (Business Profits), paragraph 9 of Article 10 (Dividends), paragraph 7 of Article 11 (Interest), paragraph 5 of Article 12 (Royalties), or paragraph 4 of Article 22 (Other Income) of this Convention are met; and
(h) to the application of the provisions of domestic law regarding penalties, fines, and interest in a manner consistent with the purposes of this Convention.
They may also consult together for the elimination of double taxation in cases not provided for in this Convention.
4. The competent authorities of the Contracting States may communicate with each other directly for the purpose of reaching an agreement in the sense of the preceding paragraphs.
It seems likely (to me) that apparent inconsistencies between:
- the language of the treaty, on the one hand, and
-the interpretations offered by the Technical Explanation and various IRS publications (not to mention a common-sense understanding of the intended purpose of the treaty), on the other hand,
are largely due to the situations described in Article 26(3) and its sub-clauses. There is no need for a UK-resident US citizen to resort to claiming IRC tax credits/reductions on exempt income such as a UK government pension, unless it's useful to them to do so - for instance if by doing so they're able to reduce US tax due on other, non-exempt UK income.
Of course it goes without saying that these comments are merely my personal interpretation.