[mothered]

Update!

Today I wrote to US support (no live chat in my country). I was talking to the same guy that wanted documentation. I gave him information list and photo with SN and handwritten ticket number. Claim is approved and I have to wait for e-mail containing replacement details.Rep just probably forgot about documentation from shop so I got lucky.

Logitech are usually firm with their assessment, so you're pretty fortunate that the rep didn't refer to the document.

All In all, the SE succeeded regardless of how It was done.
Congrats, good work.