Yeah that's totally gonna scale, not. Problem is you can't really prove anything for sure. For example, that would be a nightmare for people or businesses that want to use a single address, like a laminated QR code etc. The only solution is to generate a new monero address for every transaction. That would work and fix the trust issue but the whole scheme does not scale.
 
That is why tok keeps preaching about the value of transparent blockchain tech like btc and Dash, it scales.

For proving a transaction as a sender, it can be done on a per transaction basis. You only need your tx private key, the transaction id and the address you've sent the coins to.

For the receiver, you indeed need your viewkey which shows all your incoming transactions, but work is being done to create disposable addresses. This will enable users to have a unique address for every service/person/website/... they interact with.

edit: and as I said, you usually will force the sender to prove he has sent the transaction. So I don't see any privacy problem.

edit:
I don't see your problem with "scaling". The sender can always prove he sent the transaction.

You're welcome and that's correct.