that is sadly not really true. brown sugar, palm sugar, rock sugar and so on are different in taste and texture from white (refined) sugar.
brown sugar, rock sugar and palm sugar also have a higher mineral and micronutrient content. so they are more nutritionally viable for sure.
but actually brown sugar has more calories than white sugar, ever so slightly. all the sugars, and hfcs, and honey, have very similiar calory ratios.
they differ chemically in that they're all made of different ratios of fructose and glucose, while some other sugars also have maltose. those all work slightly differently and iirc have different effects on blood sugar levels.
your friend is still not "wrong" per se. palm sugar and brown sugar have more "good stuff" (I hate bastardizing it like this..), aka nutrients your body can actually use. it will still make you fat. refined sugar has most of the nutrients removed and is what is commonly called "empty calories" - makes you fat without giving you nutrients.