But their $7.15 was late, and apparently they're mad as hell and they're not gonna take it any more. I paid them $40, which covers the $7.15 I owe, the $4 and change for the following month, and enough more that I can ignore them for several more months. The nice lady cheerfully reactivated me.
For the record, TTI has generally been quite a good carrier, so I'm not gonna hold this against them. They are also owned by neither AT&T nor Sprint (last I checked) which is why I started using them. The whole situation was funny more than anything else, though if I'd really needed to make a call it would have been less funny.