To me, it's a bit like playing tea with the stuffed animals. I can claim to pour some tea into your cup, and you can accept that I've done that, but it's all just imaginary.
I don't think this is much different than most monetary transactions today. While some people still pass about physical pieces of paper, probably the majority of monetary exchanges now are done as simply twiddling some bits in a computer somewhere. Credit card, debit card, bank balances, transfers etc. All are accepted because the rules for twiddling the bits is established and people trust the twiddling happens according to the rules.
I don't see a difference here: the rules encompass a distributed network where the veracity of the twiddling is verified by key signatures and the statistical math that makes a false twiddle (split of block chain) very unlikely. There is still a regime of credit/debit balancing going on.