We were somewhere around Barstow, on the edge of the desert, when the
drugs began to take hold. I remember "The Medway Handyman"
saying something like:

I think I understand that. I think it means "Incidentally claiming VAT back
on stuff that is not passed on to a third party is also fraud".

I understand it is complete bollox.

Of course it's ********.
If I, as a VAT-registered entity, buy something with VAT on it and keep
it for my own company use, I'm perfectly entitled to claim the VAT back.
I registered for VAT, bought a van, claimed the VAT back, then
de-registered the following year. VATman was not happy, but it was quite
legal.
Apart from the upside of getting the refund, I found VAT to be a total
pain in the arse and my customers didn't like it either.