This above statement is the relevant bit...... the rest does not really matter.
Until last year I looked after the VAT for a UK manufacturer that exported 90% of everything they made. HMCE did regular visits as our work was very "complicated" both VAT and export/import wise. We always had large VAT reclaims each quarter.
We used to build "kit" that could be shipped anywhere in the world, could come back to us, go somewhere else, and of course got paid for from another country. Then of course we also installed, maintained and serviced the "kit" where ever it was. One of our UK service contractors would always invoice us including VAT no matter where they did the work in the world (including Ireland, were we did a lot of work too). I did point out that the services were often VAT free, but their attitude was, it didn't cost us anything (because we reclaimed it), and they'd rather charge it than have the VAT office decide they'd got it wrong.
Sometimes it does not matter if it is charged, even if it may not have to.... it is more likely to cause problems if it is not charged when it should be. (I've never seen the VAT office worry about VAT being charged in error, only when its not charged!)