Mk1 eyeball tyre check process:
Is there a distinct boundary between the tread wear indicators and said tread?
No = drive straight to a tyre shop having phoned ahead.
Yes = can you feel it with a finger nail edge?
No = drive straight to a tyre shop having phoned ahead.
Yes = research tyres according to preference and budget and get it booked in.
As an aside, I had The Barge pre Motd a couple of days before going on holiday and about 6 weeks before it was due. Was told it would pass if they tested there and then but that the rear tyres needed replacing soon as they were fast approaching the wear indicators. (I knew this before presenting it).
After a discussion with the tester, it was decided that they ought to be OK for the 500 miles that I knew I would be covering before I could get them done. (flights/weekend/an appointment in Norwich). Whilst away I got it booked in for the Monday after my return. The tyres ended up being good* for 350 miles.
*Good being a euphemism for legal. They were noticeably less grippy from about 2.5mm and fell off a cliff in the last 500 miles.
Point being that you should err on the side of caution.
James had to pay some Stupid Tax for waiting for the fail. A quick word dropping it off could have seen tyres fitted before they tested it, and therefore no issue.
It feels out of order because you felt pressured into the purchase, when in fact you knew full well that a pair of tyres were imminently required, and therefore not a surprise. At the end of the day, the car got a free MoT, and two new tyres that it needed, so you're probably still ahead on the deal