Well - it would not have to be a 'public' API per-se. A private created-just-for-the-purpose API just for IFTTT to call would work for them I'm sure.
Of course - this takes work on both ends. IFTTT has a page to get in touch to begin the process.
https://ifttt.com/platform. I'll take this moment to encourage you to get in touch with them - if you also feel a 'connection' would be valuable.
They DO have an API - but only make it available to partners it seems. I think you have to get in touch with them to begin.
Michael.