No, you can't.
In GT you can pick a lesser car and finish the race at roughly the same time as the AI. That's the close racing that GT gives you.
In Grid you can spend several laps going wheel to wheel with one other driver, finding where they're slow, setting up a pass, defending from them, and so on.
GT does not offer this. You will always be faster than the AI if you have any chance at all of winning the race.
It is possible to pick a massively slower car in GT such that you're going wheel to wheel with the AI, but because of the race setup you then give up any chance of placing highly in the race. And while the actual racecraft of the GT AI isn't that bad, it's nowhere near the level of the Grid AI.
Grid is a reasonable facsimile of racing in a fairly clean online room with actual humans. GT is not and cannot be, no matter which car you choose. It would be possible to get decent races in GT6 if we had full control over all variables in the race, but PD doesn't give us that.
Try some PC sims.
You may find that they spoil GT for you, or you may find that it makes you more adaptable and able to enjoy a wide range of levels of physical simulation.
GT is not the pinnacle, nor is Grid the worst available.
Correct, they have done, pretty much since the first announcement.
http://blog.codemasters.com/grid/04/introducing-grid-autosport/