Re: Yeah, shoot it
Unless you're a total clod about reinstalling your parts, you shouldn't have a problem shooting now, and then reinstalling.
The main reason the body shop is telling you to shoot now and reintall later is simple, masking. It takes time and can be time consuming to mask parts not to be painted. Additionally if you spray around the window openings, you are definitely going to have areas that will need to be sanded to accept the next coat of paint. If not done right this method will show either a paint line, or in the case of certain paints WILL affect the overall look / tone / depth of the color.
By painting the car inside first, then doing a very light mask job on the openings, you can shoot the outside with very little to no overspray on the inside. The final look will be essentially better which is your question.
The key to this whole thing is how confident / able you are on reinstalling the windshield, trims etc. If you take care you shouldn't have a problem. Another way to help avoid problems is to ask your painter to use Gloss Hardener on the last coat or two, or on the whole paint job, then wait at least 72 or more hours to let the paint harden.
This won't eliminate the possibility of chips or scratches, but will help so that it will be harder to do either.
Then take care and you shouldn't have any problems.