It is easier if you're one of the better mid majors to get into these tournaments.
Only one team per conference is allowed to be in each tournament. So that means if there are Eight teams they need a mid-major after the power conferences are filled. So being one of the better Mid-Majors really helps you get an invite. It is the reason Gonzaga, Dayton, VCU, and UConn get their pick of events.
This event, and most of the big ones, are owned by ESPN. They don't actually look for the top teams but the teams with the most fans who will watch on TV. These events are not about selling tickets to the arena but about getting people to tune in to ESPN.
It is hard to get into a specific event because you can only play in the same event once every four years. This means that teams shuffle every year to different events and the top teams get their priority and enter contracts years in advance. It is hard to get into a good event if you haven't been good for a long time.
I have a feeling they wouldn't have been in a good event next year if not for Penn State pulling out. Teams pulling out and switching events is rare and there were likely very few teams available for the last slot. The later you're added to an event, the lower your priority for the event. You will notice SWAC and MEAC schools getting added to events over the summer when tournaments just need some warm bodies for campus games.
Each event is formally sponsored by a host school or conference that sanctions the event.
There is an exemption for teams outside the mainland that allows them to play in the same event more than once a year if they are the host school. Otherwise, even if you're the host, you can only play in the event once every four years. (Example: Hawaii plays in the Diamond Head Classic every year but College of Charleston won't be playing in the Charleston Classic they host in their home gym.) This is why Buffalo hosting an event wouldn't really help the team. They wouldn't be able to play in it 75% of the time.
Schools and conferences that are the hosts of an event typically keep one slot to be filled by a team in their conference. This is why Towson is in Charleston this year and Northeastern was in it last year. Charleston gives one slot to CAA schools each year. The same is true of most of the other top tournaments: with the MAAC sponsoring the AdvoCare Invitational and Atlantis being sponsored by Conference USA, for instance.
Schools are often paid to be in an event. But the payments are not always the same for each school and often times they only cover expenses. It all depends on how vital you are for an event. The winning team of the Battle 4 Atlantis was paid $1 Million in the early years but once the event was established they stopped doing that. Not Teams are only guaranteed Travel, Lodging, and an appearance fee of about $150k for playing at Atlantis.
Some bracketed events don't pay teams anything other than covering their expenses for the event. They simply sell them on the location and the TV exposure.
Playing in the minor bracket and playing road games can generate teams more money in some events. The visiting team is often paid for their road games while the major team may be paid to be in the major bracket, or if they are not a big enough name, simply be provided with a home game or two in lieu of payment. When you see a four team bracket as a part of one of these events and one team seems like they don't belong, there is a good chance that they are basically paying for that luxury to get to play the other teams. And when you see a historically good school in a minor bracket, it is likely because they wanted to take the money.
For instance, it is common for a visiting team to be paid $80k to play in a four game event and then that team have to play two road games at an opponent's gym and then they get two neutral court games against similar tier teams. Hotels will be paid for but all other expenses the team is responsible for. While that might seem like an alright deal, this same school will most often be paid $85k for a single game when the go to an opponent's gym for a single game. So they are making less than they would normally make for a road game.
This is the big issue with mid-major schools. Do you take the exposure or the money? If you take the exposure, you really don't want to go winless in the event.