Amps, Cables and Current: A Question

Hi folks. I have a few questions I'm wondering if you can help me with....

1. I've seen some amps, such as the Odyssey Monos, that list peak current capabilities around 65 amps. How is it possible to deliver that kind of current when the unit is connected to a wall outlet that is fed from a 15amp circuit?

2. I've been having a email dialogue with the folks at Audience. I'm still confused by their response. According to them, "the Audience power cords need to be thicker because they carry so much current. A power cable the same diameter as the Au24 speaker wire would be a fire hazard" because it would not be able to carry all the current coming from the wall. They continue by pointing out that the speaker wire can be thin because it carries much lower current than the powercord.

If you understand what I've said here I think you can see my confusion. If an amp like the Odyssey is putting out 65 amps of current then that far exceeds what is coming out of the wall and therefore my thin little Au24 should be melting or causing a fire or something, no?

I'm no electrical engineer, obviously. I have to be missing something. Can anyone help?