Its not a complete crock of shit, but probably is in your scenario if quoted by National Tyres.
On-wheel balancing is a ‘thing’ and normally recommended by manufacturers as it allows for the tolerances of the wheel centre bore and the hub, and I think also as it includes the brake rotor in the balancing.
My Iveco van has (had, as I removed them) a pin on each hub that locates into a hole on the wheel that ensures the wheel and hub are always clocked correctly, so the studs/bolts always go back through the same holes in the wheel, keeping the wheel and hub assembly balanced and minimise radial run-out.
When replacing two tyres on your vehicle, we recommend fitting the new tyres to the rear and moving your partially worn tyres to the front.
I can’t work out if they wouldn’t fit the new tyres to the rear despite their own advice recommending it, or if you don’t agree with them insisting on fitting new tyres to the rear?