I think it's a fair definition. If you are running it from home, should you also create your own ISP to be able to call yourself "self-hosted"? Your own power generator? :)
Maybe what bothered me about the section I quoted, is that they're explicitly using the free tier and allegedly didn't give the hosting company (Oracle) any billing information. So they cannot possibly be paying for their use. It's sorta not really theirs but, instead, a charity from Oracle (there's three words I never thought I'd put together)
Does it? This is not the definition I've come accustomed to.
If "self-hosted" now includes cloud-hosted, then what should we call things that are actually self-hosted? The distinction matters. We should have a term.