Yes that's all true, and Hollywood in general is always very effusive about UK technical crew being amongst the best in the world.
And big US productions will like to use foreign locations for shooting - as well as some of the scenery being what they don't have at home, and the tax breaks other countries give for shooting there, when it comes to selling the programmes abroad, it also helps that those countries feel in some way involved.
That's all great, and certainly for the UK we need to try and use that as a kind of springboard to up our own national Film & TV production.
Apart from the financial aspect, culturally important too, because you don't always want to be looking at the world through the lens of Hollywood/the US.
I accept that UK broadcasters don't have the same money to spend, but the gap is narrowing, and this is because there are more co-production deals going on.
In the old days (i.e. 5 or more like 10+ years ago) the BBC would commission, say, a six part drama. They'd spend about four or five million tops. It'd satisfy the domestic audience and maybe they'd get some foreign sales, which was all a nice bit of bunce on top.
Nowadays, the BBC will work with HBO/Amazon/Netflix/Hulu/Showtime/Apple+ and between them, they'd spend more like 18 or 20 million on a six part series.
The Yanks like shooting here because we're non-unionised, speak English, the dollar goes a long way, and there's tax breaks. We're also low on red tape, compared to pretty much any other EU country.
So the BBC has sort of been saved by economics, but unlike HBO etc, they lack the balls to commit. Which is why 'domestic' drama tends towards short runs of three to six episodes and mostly doesn't come back for series 2.
HBO at the start of Thrones made the decision that 10-episode series and at least six or seven series is the only way to really build up an audience. And it worked. Spectacularly, when you look at the worldwide numbers.