Hi mate,
You should get him to have a read of GN8 then mate, coz he's got it wrong
I'm not criticising him, by the way, a lot of people have got this idea that you have to TT an outbuilding, but it's all rumour.
There may be some circumstances where it would make more sense to TT it, but that's a judgement call by the sparky on the job.
The other thing worth mentioning is that, if there are no extraneous conductive parts in the outbuilding, and therefore no bonding requirements, then you can simply run your SWA supply to the outbuilding, utilising either the armour, or a third core, as the CPC - once again, regardless of the type of earthing system of the main installation.