Puzzling thing about QFT in curved space-time

[ShayanJ]

In the page http://en.wikiped
ia.org/wiki/Hamilton%E2%80%93Jacobi%E2%80%93Einstein_equation, under Shortcomings of four-dimensional spacetime", you can see the following line:

It is possible to formulate quantum field theory in curved spacetime, yet even this still cannot incorporate GR because gravity is not renormalizable in QFT.

Is it correct?

If it is, how can it be? Because in GR, gravity is space-time curvature!

 

[ChrisVer]

You can have how fields interact in a given curved spacetime.
You cannot solve for that spacetime (in order to let the metric be a dynamical variable).