I gave the translation "They are our friends' friends." It said I made a typo and suggested "They are our friends friends." (Without the apostrophe marking the possession.) I think my sentence is correct. I considered reporting the mistake but did not see a corresponding option so I write it here.
See the declension table https://en.wiktionary.org/wiki/p%C5%99%C3%ADtel#Declension
You're quite right that "friends with our friends" and "friends of our friends" are used interchangeably in English.
However, the Czech sentences uses "našich přátel," and that construction is in the genitive case. So "OF our friends" is closer to the original.
But you could try reporting your version as My Answer Should Be Accepted. If it becomes an alternative translation, you'll receive a nice e-mail from Duolingo!