Depends on a few things; chronologically:

a) the insurer;

b) what the policy wording is;

c) where the policy was incepted, ie broker, direct or PCW;

d) age of the car;

e) other 'mitigating' circumstances.

That - or all of the above - said, there are some legal angles, as well as consumer rights which can get you the desired result (OE parts). It's largely dependent on what you agreed to before the policy was incepted (and even that can be challenged if the issuing broker/insurer did not follow protocol).

Also, despite what anyone tries to tell you, the best available parts are OE. With rare exception, if the windscreen (or glass) does not bear the vehicle manufacturer's logo/emblem/name, it's not as good and probably has not been manufactured in the same country, never mind plant. One of the biggest misconceptions in windscreen branding is spread by the fitters who are merely regurgitating what they've fed on by hearsay. Chinese Whispers on the intertubes does the rest.