No two takes of any song on Fun House had the same lyrics.
Iggy liked to sing live with the band in the recording studio, letting the music guide his performance. He'd start with simple ideas and improvise the rest. That's probably why the lyrics aren't so much a narrative, but rather a series of lines that don't make much sense on paper.
Since there was no structure or arc to the lyrics, Iggy could stray from them without disrupting the overall message of the song. It also gave the band a range of choices when deciding which take would make it onto the album.
This is a technique that Iggy would continue to use well into his solo career. David Bowie, who produced two of Iggy's solo releases and witnessed this process firsthand in the studio, was greatly influenced by this improvisatory technique, using it on his own songs, like with Heroes."
But it didn't stop at Bowie: This aspect of Iggy's songwriting is a big part of what influenced so many generations of musicians. They were inspired by his total submission to the music, and willingness to let his subconscious emerge without any concern for societal boundaries.