Not strictly true (as far as I know). I believe the key point is that the update must be signed with the same key as the app you are updating.
F-Droid ship apps built and signed either by themselves or by the app developer. Updates from other stores won’t be signed with these keys so can’t be installed.
Aurora Store and /e/'s new App Lounge both get apps and updates from Google’s Play Store. (Only non-OSS apps in the case of App Lounge. they still get FOSS apps from cleanapk.org, though they say they are planning to change and get them from F-Droid). So it should be possible to update an app that was installed from one of those apps using the other app, as they are getting the same updates, signed with the same keys.
The same may be true of /e/'s original Apps store: it gets all its apps and updates from cleanapk.org, and nobody knows where they get the apps and updates from 
Having said all that, life is much simpler if you don’t use many different stores: I use F-Droid for FOSS apps and Aurora for the others. For apps that are available in both stores, I get the updates from F-Droid 'cos that’s where I got the apps. I don’t recall being offered updates by Aurora Store for these apps, but if I were offered I would decline, and blacklist the app in Aurora Store so updates are not offered there again.