They are the only announced ones. They absolutely do not have to announce players testing positive and actually can't name them without their permission. This was as much a PR move as an accountability one. This is an announcement that Alabama takes their testing seriously and immediately take precautions until they know the person is negative.
Supposedly no players tested positive though and I would imagine the entire team has been tested today (of course a big portion are immune at this point). Just strikes me as odd that the 2 head guys both tested positive. But they were going to have to release those statements as soon as possible regardless, word was already starting to leak out. I'm surprised they beat Matt Zenitz to the punch.