Everybody has off days, or just instances where circumstances misalign in just the wrong way. To pretend otherwise is silly; instead, it's the leader's/team's responsibility to ensure that those sort of off days don't lead to massive losses via redundancy & the sort of measures we're talking about here & in the OP. Firing somebody in these circumstances just acts to severely reduce morale, since we all secretly know in our hearts that it very easily could have been us.
Firing in this case just seems retributive. It's not going to bring the lost data back, and you've just eliminated the very person who could have told you most about the chain of events leading to the incident in question to help you guard against it in the future. These incidents usually sound simple at the surface level ("I clicked the button in the wrong window") but often hint at deeper, perhaps even organizational, issues. A lack of team focus on reliability/quality, a lack of communication or trust about decisions made (or not made) by higher ups, or so on.
And they are probably the single least likely person to cause a similar incident again -- that person will now likely be double and triple checking their commands for eternity.