Some days you want a thicker pot handy...just to picture throwing it at the head of miserable people like your "expert" there.
Once your throwing skills are at a certain point (ie weight evenly distributed, and put where you wanted it to go), thickness is very much a personal preference. Some people like the lofty feeling of delicate wares, some find thicker wares more satisfying. Keep your work true to your voice, and the people that think in a similar vein will find you.
So down the rabbit hole we go...
I don't think you can really objectively define it. You can draw lines in the sand, but there will be an exception to every rule.
If you use the rule of "no machines", then yes only pinch/coil pots would qualify, but hey wait, what if they aren't using hand dug/processed clay? Would only wood firing qualify. or only if you cut your own wood? Do you need to build your own kiln too? Dig your own glaze materials? I don't think I know of anyone's work that would qualify.
Mostly made by hand....I think the exceptions fall in the other direction then. I visited a pottery factory in Vietnam a couple years ago. They were producing by hand to a great degree. The people doing the brush decoration were absolutely staggering in the speed and skill. However, talking (as much as I could) to the people that worked there, I got the impression that they would rather be working at the Nokia plant if they could get in. They didn't really like what they were doing, let alone love it. There work was nice uniform (with slight piece to piece variation) work, but I would definitely class it as factory produced even though it was produced by truly "unknown potters".
Personally, I think wheel thrown is fine, but extruded handles are crass commercialism.I believe if it doesn't have translucence, it's not porcelain, it's white stoneware. I believe if it's not cone 10 it's not really stoneware. Sorry, I probably insulted everyone a t least once there. Not my intent, just pointing out how they are all just lines in the sand.
I believe it's hard to define because "hand-made" is used as a euphemism to mean something more than just the means of it's production. Sadly we don't really have a word for it though (that I know of. Some use the word "art", but we're far enough down the rabbit hole already). I think often what we mean when we say "hand made" is that it is made with love, commitment, dedication, a higher purpose/intent than just to make money (insert why you make pots here). etc
When we see "crap" marketed as hand made it rankles because we know (or suspect) the intent was not of the "higher" variety.
So I think what we mean when we say "hand made" is very subjective and mostly has to do with intent.