It's solved to an extraordinarily high degree. 99.999% or greater. There are fringe cases that pop up from time to time and make headlines; the reason they make headlines, is because trillions of dollars in equities trade hands every year in the US, and such cases are very rare.

It's because there's an established system of trust, liability, responsibility, regulation and oversight in the network, assuming you're using any number of several dozen popular brokers (and that you're a common investor). Microsoft has a vested interest in knowing how many shares it actually has outstanding and who owns them; there's a chain that follows, that includes the CEO, CFO, board, other large powerful investors, regulators, common investors, and so on and so forth.

The scale and solved nature of it is roughly 100x that of Bitcoin in contrast.