Why in the world would someone go bust a (probably) teenage girls birthday party and confiscate their cake because of copyright. That is the only possible way copyright could protect it.
It's not the buyer who would get into trouble, it's the business. You need to pay for a license to use copyrighted images, characters, names, etc. Which would be hard to do, because they would need a license for every single brand they'd print.
It's like if you drew a picture and posted it on the Internet: the picture and copyright is yours, and someone can't just print your design on a t-shirt and sell it, they need your permission.
The large companies who own the copyrights would probably never find out since it's a small bakery. Nevertheless, if they ever did find out (a picture on the bakery's website, social media, etc.) than the bakery could be in a world of expensive legal trouble if the copyright owner decided to take legal action. Their just being cautious, that's all.
Why they cant put the picture of celebs on cakes?
It's like if you drew a picture and posted it on the Internet: the picture and copyright is yours, and someone can't just print your design on a t-shirt and sell it, they need your permission.
But how would they know?