I had skimmed the post earlier and came back because I thought "hmm, I wonder how he got the Arduino publicly accessible…" and didn't remember seeing anything about that.
But thanks to things like Pusher, you don't need that!
I was just picturing the request going to Twilio and then pinging the Sinatra app on the Arduino directly… But Pusher and the like really help so much to put things "online", albeit indirectly. But between a free Pusher app and a free Heroku app, it's easy to get going without worrying of your home router configuration or anything anything like that.