There was another story I read once about Katy Perry's record label sending cakes out to loads of radio stations in "celebration" of one of her single releases.

Yup, this was a real thing that happened for her 2014 single 'Birthday':

 

My point is, there are loads of creative ways you can do payola without actually doing it. Not to mention, they could simply just be lying.

 

Well yes, but payola is just a way of euphemistically representing these many different ways of 'paying for plays' - it doesn't always literally mean paying. Spotify in legal terms would argue that record companies 'sponsoring' playlists (i.e. depositing money in their account but definitely not 'paying') is perfectly fine for instance.

 

Maybe if we made a new term for it, say - doing a 'Joel Adams' - they'd be less able to wriggle out of it.

Again, note what they've actually said - "No-one can pay to be on our playlists" all the labels can sponsor their own playlists and pay to advertise them.