The extract from HMRC manuals is considering whether there might be any charge to inheritance tax on distributions to UK beneficiaries. However, it is solely concerned with that tax.
As Guya has said, there are other taxes to be considered where a UK resident receives payments from a non UK trust. The UK has a comprehensive set of rules in this area, as part of overall anti-avoidance rules. However, the motives for the setting up of the trust is mostly irrelevant and they are not disapplied because the trust in resident in the US, as contrasted to a tax haven.
In particular,the UK would tax a UK resident beneficiary on trust gains (past, present and sometimes future). There is a form of interest added where the matched from previous years, which increases the tax payable. Further, there is no relief for the US tax that the trustees might have previously paid.
Still, the UK rules give a tax burden that is generally much more favourable than the US does to US citizens receiving payments from UK resident trusts. The US tax payable in this converse situation can be eye wateringly high.