I'd guess because (1) then you'd need a visa (enjoy your couple of visits to the consulate, long queues, and grim faces), (2) he said cheap was the attraction and Moscow while a great city is everything but, and (3) he said he has a day free in London on his JER-IST trip in February so presumably would miss the LHR-IST part of his trip if he overnighted in Moscow.

Like you I certainly wouldn't try the turnaround in Russia. Too many things can go badly wrong. As mentioned by others, BA could get worried he was not entitled to travel to Russia for lack of a visa and refuse boarding to not have to foot the bill (very different from a ticket which is booked as a connecting itinerary), and Russia is such a bureaucratic system that there are quite a few people who could decide that indeed 'this is wrong' even without necessarily needing to provide a clear reason as to why they think so and still make one's trip a miserable experience, F or no F.