It looks to me that some of the above pdf is out of date. For example, it is no longer the case that UK "dividends are deemed to carry a 10% notional tax credit."

In fact, I think you are misunderstanding your US tax liability. My understanding is that, according to the UK-US treaty on double taxation, the US has primary taxing authority for 15% of any US source dividends. If you are not a US citizen then this will have been deducted at source (provided you have completed a W8-BEN). If you are a US citizen then nothing will have been deducted at source, but you are expected to pay US tax via your 1040 return, if indeed your 1040 calculation shows that this tax is due on this passive income.

The US tax can then be deducted against the UK tax (of 32.5% for the higher rate taxpayer). To illustrate: suppose you had £10,000 US dividends (and no other dividends). The US would take tax of £1,500. As a UK higher rate taxpayer you would owe 32.5% x (10,000 - 5,000) = £1,625 (after deduction of the 5,000 dividend allowance.) So the UK tax bill would be 1,625 - 1,500 = £125 after taking a credit for the US tax paid.

In the 2018-19 UK tax year the dividend allowance reduces to £2,000 and so the US tax bill would be the same, but the UK bill would rise to .325*(10,000-2,000)-1,500=£1,100.

If you also had UK dividends you can arrange the order in which tax is charged so as to minimize the total bill. Suppose in the 2016-17 year you had £4,000 of UK dividends and £5,000 of US dividends. The dividend allowance of £5,000 could be be applied to the £4,000 UK dividends and £1,000 of the US dividends, leaving a UK tax bill of .325*4,000 = 1,300 on US dividends. From this you can deduct the .15*5000=750 paid to the US. (Note that you can deduct the entire 750, not just the .15*4,000= 600 pertaining to the US dividends which lie outside the allowance.)

Finally, if you are not a US citizen and have not signed a W8-BEN then 30% US tax may have been deducted at source. However, you are only allowed by HMRC to take a 15% credit against UK tax.

A UK person who invests in something like a VUSA ETF will be unavoidably double taxed, in the sense that Vanguard will have paid 15% on the US dividends, and then will have distributed the remainder to the ETF holders, who will be liable for a full 32.5% UK tax, with no chance to take a tax credit for the tax which Vanguard has already paid.