This is about as incorrect a statement as one could make on the issue.
In any case, your definition is in stark conflict with historical usage. "Open source" was coined in 1998 when the majority of releases were as tarballs on ftp sites, and SourceForge hadn't even started. By your definition then, all of those self-labeled open source projects of 1998 didn't actually exist.
It's also ridiculous because it means that when I die, and there's no one else who wants to support it any more, then it somehow loses its "open source" status.