I agree with this reasoning entirely. It's obviously ridiculous that your lounge guest, with whom you have travelled to the airport, should have to check-in and clear security separately from you and then meet up airside. Lounge access is generally considered a greater privilege that premium check-in, so to grant the former but not the latter seems very petty.

I think the reason the rules aren't very explicit on check-in guests is so some sensible discretion can be used. Clearly just because you permit one guest, it doesn't mean you have to permit "any number of random people" (although in my experience James's guests are not at all random but very carefully selected - thanks again for that delicious dinner on Saturday); and I would regard one guest as the norm and anything beyond that - e.g. families travelling together - as discretionary and something to be prevented at busy times.

I have on a number of occasions taken a guest in Y to the Club check-in (albeit on the same flight, but not the same booking) and been told very explicitly by check-in dragons as well as check-in agents that it is very definitely permitted - even before I had any BA status when I was in CW. In fact whenever I have done this they have always given my companion priority baggage handling too and (at T4) fast-track security, without my asking. (Since the point of the priority baggage handling is presumably to prevent my having to wait, I don't think you can expect that for a guest on a different flight!).