We expect that the ratio of failure compared to the burden on society to be low and so far the real estate registry, notaries, banks, lawyers very occasionally corrected by courts of law are providing this. Even if in a few contrived, complex cases it doesn't work out, that's fine.
Here's an example: I am a resident of Vancouver, Canada and last year I was buying a house in Hungary and I needed to empower my brother to act as my agent, and, repeat, I was the buyer not the seller and yet to give a power of attorney that is recognized for real estate contract purposes I needed a "strong" one: either one with an apostille which you can't get in Canada or one sealed by a consul of Hungary. The honorary consul in Vancouver was on vacation. So my options were: visit the honorary consul in Seattle, visit a notary in Washington State and send the document to the Corporations Division in Olympia, WA for an apostille and hope it gets done in time or fly to the embassy in Ottawa or the high consulate in Los Angeles. Lovely options, all of them. Thanks god, I actually had business in Bellevue anyways and the honorary consul in Seattle was helpful.
This is the sort of documentary strength we demand and accept when exchanging goods of high value. I have a strong trust in seals, signatures and such when backed by the court and ultimately the monopoly on violence by the state -- I have this trust even in Hungary where systematic corruption is in place. If someone debates whether I own that house in Hungary, I have the contract bearing the seal of a lawyer to show I bought it and the title in the real estate registry shows that the previous owner was indeed the seller. That's the chain of ownership. Could you bribe the real estate registry? Sure, I did in 2008 to expedite the copying of an important piece of paper (that's Hungary for you, no express processing available) -- but I have serious doubts of the possibilities of bribing the registry to falsify the title as there is the chain to show it false.
Meanwhile I have zero trust whatsoever in a piece of software. I am a senior software developer / architect / whatever you want to name, and I know how this particular sausage is made and I would not trust it too far.
We could create systems that fail in even fewer cases but as always with engineering as you get closer and closer to 100% precision, costs skyrocket. We could demand that ten good people testify to your ownership like a minyan for The Mourner's Kaddish but society, so far, is satisfied with the current system enough not to do this because it would be terribly onerous.