That's not quite the same as freezing your brain for an indeterminate amount of time (decades? centuries? millennia? forever?) and expecting a spontaneous reboot after transferring and read-out + a whole bunch of other unknowns.
That's a brain that was still almost the same brain as the one in which the electrical activity as we currently detect it was lost.
Nobody actually expects this. You can't just thaw someone and reperfuse them. Extensive repair work has to be done at the nanoscale.
In any case, the evidence shows electrical activity doesn't really matter when you're only concerned about long-term identity. Electrochemical impulses don't encode memory or personality. If they did, it would be pretty clear in people who recover from extreme hypothermia, as they would have retrograde amnesia.
That's a brain that was still almost the same brain as the one in which the electrical activity as we currently detect it was lost.