The US can’t tax the UK State Pension because it’s already been fully taxed by the UK. If a US citizen reports it as taxable, and doesn’t claim credit for the UK tax that they’ve already paid, that’s an unfortunate mistake.
So it doesn’t really matter whether you think the wording of 17.3 is correct or the Technical Explanation is correct: the US can’t tax it, whether you report it as taxable and claim credit, or exclude it from taxation.
OK, I’ve an extra hour today and I’m bored anyway, so I’ll play the silly games.
First, if the UK SP is to be exempt, it must still be reported on the 1040 somewhere, and, as you propose, it’s to be exempted by an 8833. (US SS, although exempt from US tax, the gross amount received is still declared on line 20a of the 1040/2017 version.) What treaty article are you going to claim which states the UK SP is exempt from US taxation by the treaty and what are you going to give for an explanation (cite) on line 6?
Second, let’s consider Jane, a USC resident in the UK who has a £4,000/yr. UK State Pension in addition to an £9,000/yr. UK company pension which she began claiming several years ago (Jane is less than 65 years of age but UK rules were different at that time). Jane has no other income, worldwide, from any sources. The UK State Pension is taxed through the UK company pension, as normal.
Since there are no 2018 IRS tax tables available yet, we’ll use 2017. Jane’s 2017 UK personal Allowance is £11,375 (computed for the US tax year 25% 16/17 and 75% 17/18) and therefore £1,625 of Jane’s income will be taxed at 20%, or £325, which equates at 2017 IRS rates (1.24) to $403 to use as foreign tax credits on 1116.
Jane’s gross UK income of £13,000 equates to $16,120 at 2017 rates. The 2017 standard deduction equals to $6,350 and the personal exemption is $4,050, which totals to $10,410 and leaves a US taxable income of $5,710. At MFS and using the 2017 tax tables, this equates to $573 US tax due.
$573 US tax due minus $403 UK tax credits on 1116 leaves Jane owing $170 to the IRS.
Even at the 2018 increased std. deduction ($12,000 MFS and no allowable exemptions) but using the 2017 tax table since it’s all that’s available, Jane would still owe the IRS $10.
NOW, if, as you claim, no US tax can ever be due since the UK SP was fully taxed, where does the $170 IRS tax due come from since the UK SP contributed, along with the company pension, to the total amount of taxable income in both countries?