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In privacy and security settings I switched Opera to delete all cookies and wrote down few allowed sites, but despite that Opera deletes all cookies, also from sites I added to white-list. On Firefox such option works as intended, is there any way to do it on Opera too?
Wow, thanks, now I get how it works, I knew there must be some simple way to do it. 
Adding [*.] before URL.com does its job pretty well too. I should have paid more attention at the start. 
Hey, if still someone's interested in this bug I know how to semi-fix it. You have to open Privacy and Security options and go to PDF documents pad. Here you have to turn on downloading .pdf files instead of autoopening them in Opera. Thanks to this action pdf doc embedded in the frame on the site gonna turn into URL and you will be able to save this page in .mhtml, just without pdf inside.