Just...no. There is a fixed amount of energy available to airborne objects in a dogfight, and most of it comes from the initial velocities of the objects at the start of the encounter.
Which is (somewhat) true and doesn't invalidate what the original poster said. The implications means you're both right and both wrong, as it means that close in a missile can have a manoeuvring advantage as it's slow, has lots of engine thrust left (no, it's not only the initial energy that counts, far from it, a slow missile manoeuvres by pointing it's motor in the opposite direction of travel). That said, since it's chasing something, it has to be able to pull much higher Gs to just keep up.
At longer BWR ranges though, the tide turns. The missile has burned out and is moving very fast, so an aircraft with any agility (fighter) can easily outmanoeuvre the missile by just turning perpendicular to the missile's flight path--since the missile has to pull a large lead if it is to have any hope of hitting the aircraft--and then make an out of plane manoeuvre (dive) when the missile has committed. It'll overshoot by a "mile".
This is an inherent problem with long range missiles today, i.e. they're too fast and has no ability to manoeuvre at the end of their range envelope. (Note that it's not a question of energy, they have plenty of energy, they just can't turn it into useful work.)
The hypothetic, non-disposable, missiles you hypothesise about, are just that for now, i.e. hypothetical, and I can't see that anybody would bother with them, for a whole host of reasons.
While I have no doubt that "missiles" will eventually soundly beat fighters and make them in some sense obsolete, we won't be calling them "missiles" at that point, but "drones", and they'll look much more like today's fighters than today's missiles. The basic laws of aerodynamics will see to that. A rocket motor in a tube, ain't it...