Driver moderator here, and I have worked that queue for many years, so let me tell you what the slip and the numbers actually are from the driver's side, because your sister is right to ask and most passengers never do.
The direct answer first. The slip is a dispatch record, not a ticket and not a receipt. When you press the machine it pairs you with the next taxi in the supervised rank and prints two things: the bay or lane you walk to, which is the big number, and the registration of the taxi you are being given, which is the small one. The airport keeps the same pairing on its own system. So if you leave a phone on the seat, or a driver does something he should not, the airport and the Department of Land Transport can find exactly which car took you, from that slip, in a minute. That is why an old regular keeps it until she is unpacked. It also means a queue driver has no reason to argue about the meter, because the whole trip is on record against his plate. That is the real reason the level 1 queue is calmer than the street. The driver does not need the slip and will not usually take it.
The bill has three parts and they are all legitimate. First, the meter, which starts at 35 baht and then runs by distance with a slow traffic time charge. Second, the airport surcharge of 50 baht, which is a fixed amount every taxi taking a fare from the official airport queue adds on top of the meter, and it is set by the rules, not by the driver. Third, the expressway tolls, which are on the passenger on every Bangkok taxi, airport or not. The driver pays them at the booth and you pay him back. Into central Bangkok that is usually two booths. So your March bill of meter plus 50 plus tolls was exactly what it should have been, and you can tell your sister so with a straight face.
Two things to know so nothing surprises her. If the driver offers a fixed price instead of the meter, even at the queue, that is not how it works and you can say "meter, please" and he will run it, or you can go back to the desk and take the next car. And if the driver asks whether you want the expressway or not, that is a real question, not a trick: the expressway costs the tolls and saves a lot of time on most days, the ordinary road saves the tolls and can take much longer. Most drivers will ask, and either answer is fine. The rest of the mechanics, including the surcharge and toll rules in one place, are in getting from Suvarnabhumi into Bangkok, and the meter side of it is in Bangkok taxis.
One caution. The surcharge figure and the toll amounts are set by the authorities and they do change from time to time, so treat my numbers as current for now and check the notice at the queue desk on the day, because it is posted there.