I found this song..

[TheBik]

I'm not seeing too much connection either. The thing that throws me off the most is that they keep referring to "Cute Machines".
I doubt the concept of cute even exists in AAMFP.

But on a similar vein, I might as well share a song that makes me think of A Machine for Pigs when I listen to it.

http://www.youtube.com/watch?v=uAOWngxoEgg

If my personal theory that the Machine will be sentient turns out to be true, this song could almost be seen as the Machine taunting Mandus. Which I find kind of awesome.