No, I don't work for the DoE, but as a tutor and test prepper, I do work with many families who go through this process each year. I have had families choose only one or two schools and not get in, but I have also had families do the same thing and get in. Given what you've heard, this should not have happened. Furthermore, even though the DoE is no stranger to lawsuits, I can only imagine the number of suits they would be facing if the rumors were true--enough to go bankrupt, I'd imagine. Still, you should do what is most comfortable for you.
The G&T handbook makes no mention of waitlists, and to my knowledge there is no waitlist. The handbook describes an "attrition round" which is used to fill seats that become available in G&T programs after the offers have been made and accepted (like kids who move or get spots off of Private school wait lists over the summer). That round is only open to students who did not accept any placements.
I hae never heard the story about kicking out apps of students who only make one selection. That sounds paranoid, to be honest.
Who knows the truth? Notwithstanding this, I would not put down any schools that you would not send your child to. There is, I believe, a good deal of juggling and shuffling done by the DoE, and if you put down a school that you would NOT send your child to, the DoE may well offer you a spot at that school because (1) they will have fulfilled their duty of providing you with a G&T seat, and (2) there will now be a possible extra seat at one of the schools you listed and would have sent your child to, but that seat will now go to someone else who only put down the schools they would actually send their child to. I am pretty sure that the "lottery" is not a real or a complete one.