You're right. I've built pretty complex offline first web applications (using Indexeddb, Service Workers etc) initially on Chrome but when I tested them on Firefox and Edge there was just one minor bug on Edge (Indexeddb expected undefined but was given null in one case, Chrome and Firefox did not complain). So it definitely is possible to build sites that work on all browsers.
Maybe "use Chrome" means "not tested on Firefox and Edge?"
Maybe "use Chrome" means "not tested on Firefox and Edge?"