For the most part epigenetic traits seem to be transmitted by DNA too. Rather than being encoded in the pattern of base pairs, the epigenetic changes are made by slightly modifying the structure of individual bases. Think of it as adding tags to instructions.
We do not totally understand how it works, but there are heritable traits not passed via DNA - the one often in the news is women with emotional trauma pass that trauma on to their children, and those children show those symptoms even if raised in a happy home with 0 contact with the mother.
It is a philosophical argument, not a scientific one. One which if we try and reason based on how special nature treats embryos quickly falls apart anyways...