@Draug
"OK, so any good backup of the wallet, even an old one, could get its balance rebuilt?"
There is no such thing as an old wallet. Allow me to explain with a simplified version:
Let's say you, me, krellin, and PE wanted to form a currency that only the 4 of us would use. We'll call them Points. Let's each start with 100

.
Now, let's say I want to pay krellin for some *ahem* service. I give him 10

, but immediately we notice a potential problem:
If I wanted to cheat the system, I could a) use the same 10

to pay both krellin and you before either of you post the transaction. I would get 2 "services" but only have paid for one. One of you would have been cheated. Or, b) I could simply counterfeit points.
Both of these would obviously compromise our currency system.
The normal way to solve this is to bring in an outside authority, such as Putin, to monitor things for us. Instead of paying krellin directly, I would pay Putin and he would finish the transaction. If Putin monitors all transactions, ideally, fraud would be impossible.
There is another way though that doesn't use a central authority. Along with our wallet, we each would carry a journal (known as the Blockchain). When I gave 10

to krellin, we would both mark the transaction in our journals (which are separate entities from our wallets). But, you and PE would *also* mark the transaction between me and krellin, even though you two weren't actually involved.
In this way, all 4 of us always know every transaction that has ever taken place. Again, ideally, making fraud impossible. 3 (a majority of us) would need to cook the books in order to corrupt the system. But, at that point, there's really nothing to be gained by doing so (and that can't even be done for more complicate reasons).
So, if you lost your wallet, you would still update your journal every time krellin, PE, or I made transactions and you just would wait until, hopefully, you found your wallet again and started using it.
Does that clear things up?