I am not a lawyer, blah blah blah....
There is no problem, per se, in including the details of the Boost Software License in the post. Note that if the Boost folk feel there's been a copyright violation, they can use DMCA takedown processes to have the post removed, and that's the established procedure if things are copied inappropriately by a poster on Code Review.
Also, note that the post, just by being a post, on Stack Exchange, also licenses the specific code under the Creative Commons license (CC-BY-SA). There is no legal issue (from the perspective of Code Review) with using multiple licenses to publish under.
So, there is no reason to prohibit adding the text of the Boost Software License.
Now, from an armchair/layman analysis perspective, and reading the OP's post, and assuming they are correct in their assumptions, it appears that the Boost code on a file-by-file basis are each individually in the public domain:
// pem-rd.cpp - PEM read routines. Written and placed in the public domain by Jeffrey Walton
// Copyright assigned to the Crypto++ project.
// Modified for selective standalone use by Mako Bates
// Crypto++ Library is copyrighted as a compilation and (as of version 5.6.2) licensed
// under the Boost Software License 1.0, while the individual files in the compilation
// are all public domain.
but the library as a whole is licensed under the Boost license. If this is the case, then as far as I can tell, there is no reason to believe the Boost license is needed to publish this code here... although it is polite, and probably is a reasonable CYA thing.
If you're looking for a TL;DR - there's nothing wrong with including that text, but including it, in my assessment, does not change anything in terms of licensing the code in this post (it's CC-BY-CA - and perhaps also licensed under Boost)