OK from what I remember from teaching in the east End (and believe me, we had lots of nits) the reasoning behind the different solutions goes something like this.
Chemicals do work, but nits can be impervious to them. Local pharmacists tend tt work together so that which chemical they are using in an area is all the same, and then gets changed. That way they try to combat resistance.
Nits are actually the eggs. The eggs stick to the hair, and can only be got off with a nit comb (no ordinary comb will do). If they are not removed they will hatch, and then lay more eggs (nits). When you first have them, the eggs are very close to the scalp, and harder to remove. You have to comb very carefully, and it is hard to do on long, thick hair.
The adults are called lice, you have to have lice to get nits. Lice are quiet easy to get rid of, wet combing carefully will do it. It is easier if they are dead (from chemical stuff) but not necessary.
If anyone in the family has them, you need to treat evryrone, because they walk fomr head to head.
Our hairdresser said that if you condition your hair (doesn't need to be teatree) and you comb it very well (and that is the hard part) then there is no reason why you shouldn't get eggs and lice off. The eggs are very, very stuck to the hair though, so you have to be good.
If you use the chemical and don't comb properly, the eggs may be dead, but they will still be there. As your hair grows out, you can see them more easily, like bits of dandruff stuck to the hair, but you can't pull it off with your fingers.
Well, dont know if any of that helps, amazing what useless information you accumulate as a teacher. Probably more than you neede to know!!Hope something works for you.
OH, and you need to strip off pillowcases and was them at 90 degrees or more to kill and lice/nits wandering around!