For a group shared directory, assigning the disk space usage of files therein to one single user (ignoring the aspect of "which single user do you pick") is unfair to that user (his/her allowed maximum disk space is consumed) while everyone else is not charged for their actual usage.
This all came about to try to enforce rules to prevent one (or a few) rogue users from using up all disk space on the system for themselves, leaving no one else with any disk space available for their own usage.
That's what quotas are: per-user storage limits.
If Bob has a large file which is sitting in Alice's home directory, that counts toward's Bob's quota, not Alice's. If Bob could sneakily change the ownership to Alice, while leaving the permissions open so he could access the file, then the file counts toward Alice's quota.
(I'm the author of the linked-to article.)
I suppose it could work, but Mallory would then risk Alice blowing that file away (perhaps innocently, not even realizing it was Mallory's file).
The protocol for changing ownership should be two step.
1. The file is put into an "offered" state, e.g. "offered to bob". Only the owner or superuser can make this state change.
2. Bob can take an "offered to bob" file and change ownership to bob.
Files can always be in an offered state; i.e. have an offered user which is normaly equal to their owner. So when ownership is taken, the two match again.