6. Jessie, James and Meowth's motto isn't the motto for the whole Team Rocket organization, not even in the anime canon.

Possible holes in the theory:
1. Player catches Mewtwo anyway, because let's face it, who didn't
2. Team Rocket actually did crime jobs in Johto, long after Giovanni left. Even if Giovanni was trying to save the planet, they were likely oblivious, and thus still evil.
3. A Plasma grunt reveals that Black and White take place long after Red and Blue, and this is backed officially. Ignoring Anime canon , it would take either some serious detective work or some vision of the future for Giovanni to know of Team Plasma. And even then, if he knew back then, wouldn't he target Kyurem and use it to stop Mewtwo?
4. The player characters are revealed to be all in different times. How would Giovanni stop Team Magma and Aqua if, if my memory serves me right, he focused on Mewtwo only while Magma and Aqua were busy destroying Hoenn at the same time? Going further, Giovanni would need a prediction of over four years to know of Team Plasma and their first defeat.
5. If this were really what was happening, how the hell did he not know about Johto, a region RIGHT NEXT TO KANTO? And why didn't he try to catch Lugia or summat?
and finally 6. Wouldn't Team Rocket just use Mewtwo for their own ends? Even if Giovanni had good intentions, TR was still all too evil and thus they'd probably use Mewtwo for themselves.
So don't feel guilty about saving the world dude. You're saving it because one man had absolutely no chance of doing so. You just had to make it apparent to him.