I've read a few articles showing various scars, and saying less than 0.5 mm is "shallow",
I believe that these scars can be completely smoothed out - or at least until you couldn't see them without careful examination, and this can probably be done with TCA peels.
but depending on 0.1-05mm is the factor on how many you may need.
I had a few very wide 0.1-0.3mm scars (boxcar), and they completely flattened out with 1 20% tca peel, leaving red marks behind that faded in a couple of weeks.
But your derm might have seen scars as deep as a centimeter in his day, so when he say's "shallow" it might be in comparrison to his previous patients.
Do a guestimation in the mirror with a ruler?
shallow scars in my opinion are scars that are relatively hard to see from a distance. For instance if from a small distance they become invisible or greatly diminished, in my eyes they are shallow. Do a reflection test in a car window for instance, if you have trouble seeing very much scarring, but you know when you look in a mirror that you can see it, chances are you have shallow scarring because the way the light reflects off of the scar is not much different than your skin that isn't scarred.