I talked to him and indeed he encoded the files (I guess to save space). Well, thanks to the help of all of you now we know where the problem is. Will give it a second try soon.
Yeah, just use tsmuxer to convert the MKV into a Blu-Ray ISO (or BDMV folder), then burn the ISO or folder directly to a disc. That way you aren’t altering the video or audio in any way, and as has been said, the existing files are already 100% Blu-Ray compatible.