That is logically false; the nature of Authority is its delegative nature; as Jesus said: the one who is sent is under the authority of the one sending.
The Chain-of-Command is such that your unit's commander is under their commander is under their commander until the point where they are under the President -- any order coming outside of this chain is not authoritative, for if it is then the entire military structure is compromised. Furthermore, as the Constitution specifically placed the President into the position of Commander-in-Chief any scenario where your orders's authority do not originate from the President (or the Constitution itself, as in Art 4, Sec 4) are contrary the Constitution and therefore illegal orders.
Are you bound to follow illegal orders? No.
So having your deployment orders coming from the SecDef is either (a) because the President has delegated the authority thereunto (and thus your orders's authority comes from the President) OR (b) they represent the exercise of usurped power.
Are you bound to follow illegal orders? No.
This is correct. I have never received deployment orders since obama has been in office. Other orders I’ve received (ie day to day functioning) would have been given regardless of who was in office. All orders I’ve received have been within the battalion and thus I see them as legal orders.
Any order coming from obama would be invalid.