@Graham *****
immigrations is telling people who are "at the edge" of entry to get a tourist visa, so their travel history can be weighed upfront. Doesn't take away their discretionary right to overrule this upon entry, but will they do that? No, they won't.
Telling people only about the very extreme case isn't always the best help. People with a tourist visa should be able to trust that they can enter.
A visa is like an entrance ticket. An entrance ticket to an Ed Sheeran concert also normally gives you the right to enter it. Can the security refuse you still? Yes technically, and if you carry eighteen stilettos in your pockets they might. If not, they'll let you in.