I did not follow the BabyWise book in particular though I've read it, but I did feeding on demand with my son (born first) and parent directed feeding with my daughter (born second). I can tell you from experience, that when done right, parent directed feeding can be wonderful for both mom and baby.
With my son, I was so stressed out with feeding him every 2 hours (or less) every time he cried, sometimes he wasn't crying because he was hungry but then he would eat a little, but not enough to fill him up for longer than an hour or so. I did a lot of crying myself because I was simply worn out from breastfeeding so much.
With my daughter, I learned to tell by the time whether she was crying because she was probably hungry or if it was probably something else. And often she didn't even have to wail out with hunger--I knew when she was going to be hungry and could plan the day's schedule accordingly so we wouldn't start driving somewhere only to hear the distressed wailing of a hungry baby. BOTH babies THRIVED, but the parent directed feeding was much better for the whole family's sanity.
I think the other moms and doctors are thinking of the cases of moms letting their babies scream with hunger and not feeding them because it's not the right time. Of course a baby will not thrive if they don't get fed enough. But proper parent directed feeding is supposed to take into account the needs of the baby too. You are supposed to adjust the schedule to fit the baby's needs. If you're using a 3 hour schedule but the baby keeps getting hungry after 2 1/2 hours, then you change to a 2 1/2 hour feeding schedule. It's supposed to be used with common sense and love.
But back to your question...
It might be a growth spurt, and you'll need to feed him more often for a few days while he adjusts. Get up and feed him at night while he needs it.
Or you could try to shift your routine a little for a while. Was the first feeding at 7:00am? You could try starting a bit earlier in the morning to have his last feeding at maybe 9 or 10pm. That way he gets an extra feeding during the day instead of in the middle of the night.