First: Your example of Cid is obviously not true (as you've said), but it is true of Gilgamesh. He just can't control his void-drifting. Any instance of Gilgamesh (excluding the XI version and a few others) can be considered canon to the FFV Gilgamesh's story. I really look forward to an instance of Gilgamesh in XIV.
Second: The thing about Shinra was actually brought up in
Final Fantasy X-2 Ultimania. Shinra did mention in X-2 that he wanted to harvest the energy of the farplane, but that plan is never started during the game (unless it's in International, which I haven't played.) The Ultimania series offer official addenda to the original stories, and in many cases can be considered canon. X-2's left this scenario open as a "maybe". Personally I think the Shinra thing is far-fetched - the people of FFVII's world would have had to exist long enough to entirely forget space travel until Cid Highwind rediscovers it, and the name of a young Al-Bhed boy would likely be forgotten before then.
@Bowen: The seeds of racial integration in FFX-2 allow that Al-Bhed wouldn't readily exclude non-Al-Bhed from joining in their galactic exodus. Also consider Dirge of Cerberus: the Lifestream itself (everyone) can be carried across galaxies to take root in a new planet. Again, I doubt the name Shinra would reemerge from the lifestream.
Third: Rufus Shinra is the only legitimate son of
President Shinra (no first name), who dies early in FFVII. Rufus took over the company within the hour, and the first president is quickly forgotten by the player.