That is 'technically' true. I submitted mine –I'm a Peruvian expat– putting the info of my parents house. They did set up a conciliatory meeting with LA but LA responded before the meeting and solved the issue before, so I didn't had to attend at all.

(Indecopi told me informally, after I called them when I received the email of the meeting that, LA representatives do not show up to the meetings at all, but since the customer protection regulations call for this procedure to take place before a claim turns into a legal procedure, it would have been necessary to either show myself, or call when the meeting was taking place to talk to the non-existent LA rep.)
Sorry that this won't fix the issue for you... I wonder if there is any way for you to do a claim in the US –anyone knows?–, since I'm assuming you bought your ticket here, right?

If so, maybe the DOT has something equivalent... if sold as a single ticket from US to Peru and back, there might be a way of getting to them...