Not necessarily true. I've grown nute-free many times with a decent outcome.
It's definitely the pot size. Plants that are one foot tall should essentially have a large amount of roots. If there is no room for the roots, the rest of the plant will suffer. I'd say your best bet of saving the plant is to transplant immediately into at least a 3gallon pot and give it some type of root growth stimulator. And don't flower them yet. Nurse them back to health first. Plants use a lot of energy to create buds. If they barely have enough energy to stay alive, then you'll be back on here soon asking why your plants aren't budding 5 weeks into flower.
So what size pots are the other plants in?