Since my house was built, I have paid $225.00/yr to have it inspected or whatever they do. No problems. Now they want almost $1000 for a booster. I live in FL and have never had any problems with termites.
I'd say no. Sure, they can, suddenly, say they dropped some treatment every prior year that kept them away. But then, you say "fine I'll just pay the same old $225, since it's working so well". To me though, it sounds like they haven't been doing anything and it's time to get rid of them...especially since they won't take less than the $970.
Get another Pest Control company in and have them check any bait traps or other signs of treatment to assess whether there's ever been anything done or if there's even any threat. It's very common to find no bait traps at all or that any bait traps are empty with no signs of residual evidence of any bait ever being used. Most contractors are just termites of your money.