Key thing about the JCOS from (https://www.jcs.mil/About/):

"Today, the Joint Chiefs of Staff have no executive authority to command combatant forces."

Bear in mind, a lot of the people Trump assigned to the White House was so he could remove them from the military and appoint patriotic people in their place.

Furthermore, their claim to protect the Constitution is complete bupkiss. They know the states and Congress violated the constitutional provisions for elections and, therefore, the 14th Amendment, Clause 3 means they are NOT legally holding office right now.

Then again, the military is also only told things WHEN they need to know and WHEN they are about to happen. So, for all we know, this is mis-information to make sure all the bad guys feel good about being in DC on inauguration day.