This rule only applies to direct flight between the USA and the UK. Other flights, such as domestic flights or those to South America and/or Canada, can count towards miles and tier points. The restrictions on trans-Atlantic flights have to do with competition "concerns" as noted above.

But I have always been hazy about whether the restrictions applied to direct flights between the USA and continental Europe...

Assuming a new open skies agreement is ever reached between the EU and the USA, these restrictions should then disappear, no?