In the Pittsburgh area you may have attended a bun run or a rabbit romp in both of these events the rooms are used for multiple activities that include other types of animals. The bunnies spend the majority of their time at these shelters alone in cages (or with a bonded partner). As outlined in the question What means do rabbits use to mark and defend their territory? bunnies do have a tenancy to mark and defend their space, and the droppings at runs and romps are often attributed to this marking behavior.
This may or may not be marking behavior. Both of these events began with bunnies haveing free range in the run/romp area, making the inclusion of litter boxes challenging. Each bunny has their own litter box, so bringing a couple of personal litter boxes could lead to territorial defense issues. Bringing a couple of fresh communal litter boxes could work, but as described in What is required to house break a rabbit? half of the training is about location, so that adds problems to getting bunnies to use litter boxes that they are unfamiliar with. Additional I can attest from personal experience some bunnies get overly defensive of a litter box that they consider "theirs".
Both the run and the romp are held on pet accident proof floors, given all of this there is little incentive to actually attempt to include litter boxes at the event. As most of the droppings are solid and bunny droppings are really easy to sweep up with a broom and a long handled dustpan, it is just easier to not have the litter boxes.
Due to the potential for bunny fights the WPHS romp now keeps the majority of the bunnies in separate exercise pens. About a year ago at one of the romps I tried an experment and brought up each bunnies litter box with them, and placed it in the exercise pen with the bunny. While there was some usage of the litter box, we still saw lots of marking type behavior. There was insufficient motivation to try it a second time.
This all may be do to marking behavior, or it may be learned behavior. There is a long history of run/romps without litter boxes so, the bunnies may have "learned" to behave this way.
We we take these same bunnies to offsite events (pet stores, schools, etc) we will bring the bunnies litter box with them, and while there may be some marking behavior (and sometimes not) we tend to see the majority of the droppings in the litter box. I have occasionally forgotten to bring the litter box and have been able to keep clean floors by taking the bunny out (on a leash) to pet area to do their business every 30 - 45 minutes.
I have also been to a few "bunny parties" where groups of bunny parents bring their bunnies to someones house for a party. Depending on the weather these can be indoor or outdoor events, there is really no point in a litter box at an outdoor event (on the grass) so I don't have any real experience to offer on that. For indoor events there is generally a a couple of community litter boxes provided, and many parents bring their own litter box. The bunny and their box are set down together, and the bunny leaves from this "home territory" to visit and returns as needed (dropping or personal space).
In these events there are a lot of bunnies running around much like a romp, but we don't see the marking and dropping behavior that you do at run/romp. This may be because the "Territory" is clearly claimed by the home court bunny, and everyone else is on their best visiting behavior.
In the end, the most likely explanation for droppings at a run/romp is territory marking of area that is NOT clearly claimed by another bunny, where there is a lot of competition for this unclaimed area.