Puckish: Frankly, I am rather touchy (who said paranoid?) about computer use, and I find it highly unlikely that computer help is widespread here in backgammon games. As I said, I rather think that the case I disclosed is an unique one. It is certainly a very different story on sites where money can be won.
The behaviour you described would also fit me. Like alanback, when facing a tough move, I often like to get a night of sleep over it, and my ideas are sometimes clearer the next day. Or I see that the move requires a lot of counting, and keep it for when I have the time and availability to conduct the whole calculation.
Moreover, the way GnuBg works, it is a bit tedious to enter a specific position, while it is very easy to open saved games and enter moves one after the other. So a cheater is more likely to consult the bot for every move, even though a "clever" cheater would make himself tough to detect by introducing enough mistakes to stay with a "human" error rate.
I see that my made-anonymous accusation is likely to open speculation. So I will at least say that I have had a PM conversation with the cheater about it quite some time before posting here, so he/she know about it, and nobody else should feel that he/she could be targetted.