If anyone above is interested in follow up then here it is.
I've contacted Humble Bundle support and they replied:
In order to claim free games, you must have a Steam account associated. This is a security measure that we've enacted on the free game promotions.
So I said that I already have Humble Bundle account and asked them what kind of "security measure" requires some 3rd party account? They replied:
I'm sorry for the frustration. A Steam account is required to claim the free game content that we offer. We are unable to offer the titles without the connection.
This time they completely omitted my question about "security" and just simply stated that I need to have Steam account to get their free DRM-free games (lol). I tried to get even more details about the reasons by sending another mail but I got no reply so far.