She actually admitted that. But as Greg Proops pointed out, that the song, being called Irony, has no irony in it despite attempting to is, of course, ironic!
He also used the example in the song "Like rain on your wedding day." Rain on your wedding day, he said, is only ironic if you are a weatherman and predicted good weather for it!
A tattoo "I'm against tattoos" would be ironic if, as it is presumably intended as a humorous statement, it then gave you poisoning that really DID make you against them.