The conversion of cine to Digital can be as simple as taping the projected film under very controlled lighting conditions and capturing audio by means other than just using a microphone to record a speker output.
Even so the Camcorder used would be a high quality one regarding sharpeness and colour reproduction and one whose frame rate can match film to avoid any "flicker".
Some processes even Scan the film by a frame by frame process and then reconstruct it digitally. As you can imagine this requires a separate audio capture process
The captured footage is then "cleaned up" , enhanced and Reconstructed ( they call this "Remastering"

) before you get to see it
Major re-releases of Old films more than likely use sophisticated variants of these methods.
Also not even all recent movies are shot digitally and yet they get to us in pristine quality
As such the quality you get will vary on your original and the process used by the company.
You have absolutely nothing to lose trying to record your cine film your self ( even if it is just for the fun of trying it out)
You can then "tidy it up in software on a PC before turning it to DVD. I imagine just recording it to miniDV and transferring to DVD via settop may end up looking like some of those cheap and nasty "pirate DVDs" made by recording in the cinema on a camcorder

If however it falls short of what you want.. then you might have to do it commercially carefully choosing who to do it for you based on affordability and VFM