How the feds claim authority for indefinite detention

A commenter sent me a personal e-mail asking a question about "If this isn't unconstitutional, nothing is" from yesterday. He asked, 

I'm assuming this is referring to Executive Order 13567. I didn't read it thoroughly, but I wasn't able to find the section that claims this right on first scan.

Can you comment on which section of Executive Order 13567 claims this right?

I studied the Executive Order, and was stumped too. I consider Andrew Napolitano to be a highly trustworthy source, and was surprised that he came up with this without further backup. I did some further research. The fact is, this assertion is not new to this Executive Order. Here is how I answered the commenter:

The answer in Executive Order 13567 isn't obvious. Section 2 holds that continued detention is warranted if it is necessary "to protect against a significant threat to the security of the United States." There is no independent assessment as to what a "significant threat" is. Practically anything the President has wanted to do in this area since 1945 can be, and has been, justified on the basis of "national security."

The second warning comes from section 1(b), which that this is a "discretionary process of review" that "does not affect the scope of detention authority under present law."  The periodic review process strikes me as being the reverse of a show trial. It pretends to offer a way for the detainee to be released, but a careful reading of section 3 in light of the other two sections suggests to me that it does no such thing. It's a completely non-binding review.

The "scope of detention under present law" where it applies to foreign nationals, is vast. The issue of detention after acquittal arose in an article by Joan McCarter for The Daily Kos (not exactly a right-wing publication), entitled "Presidential Post-Acquittal Detention Power." Quoting testimony from the Senate Armed Services Committee July 7, 2009, Defense Department General Counsel Jeh Johnson gave this reply to a question by Sen. Mel Martinez (R-Florida):

Martinez looked surprised. "So the prosecution is moot?" he asked.

"No, no, not in my judgment," Johnson said. But the scenario he outlined strongly suggested it is. If an administration review panel "determines this person is a security threat" and "for some reason is not convicted of a lengthy prison sentence, I think we have the authority to continue to detain someone" under "law of war authority" as granted by the September 2001 Authorization to Use Military Force, Johnson said. And beyond that source of authority "we have the authority in the first place."

Continued detention without trial, or after acquittal, is an egregious violation of the Fourth and Fourteenth Amendments.

Questions: If we do not uphold our own Constitution, how can we say that we stand for freedom under the rule of law? And if we cannot say that we stand for freedom under the rule of law, by what moral authority are we conducting this so-called "War on Terror"?