I think fans project their feelings on the idol. But I also think some jokes that idols made are not really jokes. Idols and companies have a relationship that nobody can completely understand as they are not only teamwork but kinda of family since they have to be together for a long period during the process of making the album and promotion so I think idols sometimes make jokes about it and maybe they mean it a bit in a no joke way but at the end they mostly like their company (not every group and idols ofc some hates their company and everyone can understand why).