Not rewriting history or anything. The Mozilla Foundation made those apps to directly compete with Microsoft to offer free and open-source alternatives to the built-in apps of IE and Outlook Express, and they succeeded at that.
You're pointing out a different thing from the original comment I responded to, and Firefox+Thunderbird were in the mix years before Gmail and Chrome, and if you want to get "revisionist" about it, Mozilla had the browser and mail client as one single app prior to that in an attempt to do the same thing, which was an entire decade before Chrome was released.