It's probably finding the office space themselves, and presumably for cheaper. But this is kind of left for the reader to conclude, so I'm not sure what the message is here.
* Fire people?
* Do a cost-benefit analysis - could they sustain a new space? Or would they have to move everyone to somewhere cheaper?
* Would shifting some people to work remotely work?
Delegating getting more office space was running away from fear because it was the option that required the least thinking about his fear.
I think the CEO's overall point is still valid, but in a different way. If you are a leader with substantive responsibilities, you'll get tons of "bad feelings", and some subset of them will turn out to be real problems. One sign of a good leader is how accurate they are at predicting which ones are real problems. This is one place where experience matters a lot, because experience (applied well) helps a lot to translate the bad gut feeling into targeted investigation.
Stopping and thinking critically about the situation, questioning assumptions, analyzing KPIs, analyzing risk levels... (or delegating the above to a capable team member with the understanding that you want the truth), asking thoughtful, open-ended questions of subordinates --- essentially, opening your mind up and allowing yourself to carefully consider all potential outcomes, even the nasty ones that you would rather remain blissfully ignorant of.
As a leader, you want to believe everything is going along just fine. Sometimes when it's not, you sense that as a fear-in-the-gut, and the temptation is to ignore it. The message here is - don't.