While BigBlueButton does work through only port 80, you don't want to try and run too many connections that way.
When tunnelling (you'll see the words [ Tunnelling ] in the lower right-hand corner), the BigBlueButton client makes about 10 HTTP requests each second to keep up with the sessions.
As you add more clients, at some point, depending on your firewall, network, and BigBlueButton server, the increasing HTTP connections will not all be services.
Once the BigBlueButton server is unable to keep up with the incoming HTTP connections, the clients that are tunnelling will start to drop. (They will get a message saying "you have been disconnected")
So, HTTP tunnelling is good for the few users that can't connect from their location (usually because they are behind a firewall themselves and can't make a direct connection to port 1935).
For running a BigBlueButton server, however, you definitely want ports 80, 9135, and 9123 open to the internet so all clients can connect directly.
Regards,... Fred