most Bitaxes are mining on a mining pool like CKPool. That is not exactly "solo", but the specific pool rewards you 98% of the block reward if you solve it. You do have to trust it, though.
I don't know the technical details, but I assume you can verify your own address is somehow in the data the mining pool sends you, right? After all, if you mine a block it instantly sends 98% to your own address.