My experience is that for large enough definitions of big they definitely do. I'd be shocked if any company with a market cap of >$100B didn't for instance (there are 120 of those), or any country with a GDP > $200B (there are 51 of those). As you start shrinking to more reasonable definitions of big I'm sure you'll start collecting some outliers who don't, but I bet you have to get reasonably small ($1B market cap as a wild guess?) before the majority don't
I count "administering VMs allocated on someone else's hardware" here, since it counts for running mastodon - the real giants probably almost all run some of their own hardware, but that probably drops off much faster.