I think that what you refer to as hidden services are very different from what the SAFE Network scheme involves. The routing anonymity of the SAFE Network is not a service added, it’s the function by default. There’s not another way to do it as part of the basic protocol.
I think the post below is worth a look-see. It is not a new post so exact points may not be exactly right, but it is very good at giving how the near bullet proof anonymity and privacy of the network is achieved, between encryption and routing: