There is a link between scheduled feeding and failure to thrive. A lot of the articles I've read on it have been linked to Babywise (which is this crazy Christian philosophy and parenting approach that basically says you have to teach your baby to be on a schedule and accept they'll only get as much as you give them to eat because basically you're the boss and that will mold them into an obedient child, blah, blah, blah). That's the most extreme manifestation of scheduled feeding. It's worth having a look for some of those articles. I read a few good ones awhile back, but I couldn't find them just now when I searched. If you have more time, it's worth looking into some of the critiques of that approach and risks of failure to thrive.
Realistically, it's better for babies to be fed on demand, whenever they want and as much as they want. If she wants to keep to a feeding schedule, every 4 hours or whatever, then baby should still have as much milk as they want at that feed, not restricted to only a certain amount, which if they finish and are still hungry, they don't get more than.
I was BF still at 1 month, but I had a small baby that struggled to gain weight and nearly was diagnosed as failure to thrive (due to latch and supply issues). I don't know how much she was taking per feed at that age, but I was told to feed her at least every 3 hours round the clock in order to keep her weight up and as much as she would take per feed. That would certainly be more than 2oz every 4 hours.
When we did switch to formula at 10 weeks, I was told that I should be offering her 150-200ml of milk for every kg of body weight, which is usually the standard recommendation for baby's up to 6 months (I think in the U.S. this translates to 2.5oz per pound of body weight daily). So for instance, at 1 month, my daughter weighted about 3.4 kg. So that would have been about 510-680ml per day, which is about 17-24oz. 6 feeds a day (if your friend is feeding every 4 hours 24 hours a day) would be about 2.8-4oz per feed (obviously, that's based on my daughter's weight and she was small so may vary). I think she would have taken more in the range of 2-2.5 oz per feed, but that was usually every 3-3.5 hours, so we had roughly 8 feeds a day usually, give or take. My daughter was not a big eater, so definitely would have taken less than others did, and she was small. But we just narrowly missed being diagnosed as failure to thrive by about 2 days because she re-gained her birth weight just shy of 28 days. If your friend's baby is taking less than this, I can definitely see why there are weight issues.
