He may have been refering to things like maintenance penalties on large ships, which realistically do not make sense. Why would something cost more to maintain just because it is housed in a larger hull? It would not.
Also, with proper QNP, small ships do not actually go faster, they go the same speed with the same fraction of hull space devoted to engines. They use the same fraction of total fuel per turn for that movement too. They do use more supplies per sector of movement, yes. But, they also store more supplies. A ship 2x the size uses 2x the supplies. But, it also stores 2x as many supplies, so it evens out. The advantages of small ships are that they require fewer resources spent on engines to get the same speed and they require fewer solar collectors to get infinite range (or fewer solar collectors to extend range by the same amount), although again, the same portion of hull space is required to get the same effect on max range of the ship.
Here is an example:
2 ships size 300 and 600 require, say, 10% of hull space to get 6 movement from engine type X.
6 engines x 10 supplies used = 60 supplies per sector
6 x 500 supplies stored = 3000 supplies
3000 / 60 = 83.3 sector range
12 engines x 10 supplies used = 120 supplies per sector
12 x 500 supplies stored = 6000 supplies
6000 / 120 = 83.3 sector range
So as we can see, you can get the same speed and range out of any two different size ship hulls in a QNP system. Of course, there will be very slight variations due to rounding in integer math, but those are not significant in the big picture.