One point in the piece is about how the clubs would use these facilities when they were not being used by varsity teams. Which is true, however, my bet is they would need to staff the facilities during the club sports times. If permanent employees staff the facility and not students, the school might face overtime pay as well.
Secondly, and this might be easy for me to say, but if a school is getting tremendous number of requests for use of varsity space, it would actually benefit the club to pay for the space (if they can afford it). That way they can guarantee they get their time. Otherwise, the space may become diluted over large numbers of clubs, and a team may only sees the space once a week. Schools are usually afraid if they "do something for 1 they have to do it for everyone" - but if they charge that deters a backlash for opening the space to the serious paying clubs.
Preparation is the key to handling this in the future - hopefully it won't cause too much trouble this year.