you have those rights whether or not anyone reads them to you, you should always be aware of that. the miranda rights warning is an additional thing that was added to ensure that people were aware of their rights, but it is not required by the constitution, it was simply a good idea that was added to help ensure people being arrested were aware of their constitutional protections.
if you're not read miranda rights, a good lawyer can exclude any statements you made after arrest from evidence. that's the extent of their power. complaining that your rights weren't read to you means nothing unless you're making a motion to exclude a statement you made after being under arrest. that's it, that's their whole power. don't rely on them being read to you, know them yourself. the cops won't bother to read them to you unless they believe that they are going to need to include your post-arrest statements in order to prove their case, and even then probably only if they expect you to have a decent lawyer or something.
which is why this "public safety" exemption is not in and of itself all that crazy (what was crazy was the idea of calling him an enemy combatant or something), so long as no statements that were obtained prior to him being informed of his rights are not admissible as evidence against him. the idea behind the public safety exemption is to obtain information not for the purposes of prosecution, but for the purposes of trying to stop another attack basically.