Edit: And I don't know how to send bitcoins to my phone number
I don't see how it could be the latter. You are sending them an sms, they have no way to access a private key on your device.
This is what I'm finding confusing. Going by the limited information on the site alone it says: To make a transaction simply text your request. ex. "send '555-phon' 10 for beer".
Please bear in mind I may have got this totally wrong because I am not a techie. But my understanding of that is that you're sending your payment SMS to the service provider not the recipient - in which case isn't it just an on-line wallet service with SMS instruction for payments and SMS notification of receipts? If so then the private keys of the wallets associated with the phone numbers surely have to be kept on the service provider's side. In which case, my question is: Are they only accessible via instruction from the phone or does the service provider also have access to them. Unlike Blockchain.info wallets where the encryption/decryption can be done on the client side I can't see how that could be handled by an sms-only phone.
I'm not saying the service provider is untrustworthy but if my understanding is correct one essential aspect of Bitcoins - i.e. not needing a bank - is absent. Maybe paywithbits.com is more trustworthy than Barclays or Mpesa? I don't know but it's a big step away from what in Bitcoin world we're used to and I'm reservedly excited about this as something I'd like to see go viral in developing nations until I understand more.
The no bank aspect isn't what will win the masses. As long as they are competent with security, I don't see a problem unless they aren't upfront about their real identities. The need to be a registered business with the proper licenses. Bitcoin is great for those of use who know how to secure it ourselves, but the average person is scared they will get hacked and lose it all.