Dazzled and confused about xparse and LaTeX3 Booleans

Dazzled and confused about xparse and LaTeX3 Booleans

I'm just starting my journey with LaTeX3/expl3, and although fascinated by
the great work that the LaTeX3 team is doing, and by the enormous
difference it brings about with respect to "classical" (La)TeX programming
(to me it's such a nice experience that I'll try to stay within its
domains as much as possible), I'm still a bit confused on some points. One
of those has to do with the \*DocumentCommand family introduced by the
xparse package.
So far I had been using the members of this family embedded in a
conventional LaTeX2e setting, just toying around with their rich
parameter-setting structure and, some mishaps out of lack of practice
aside, had no trouble. But now I'm getting eager at having LaTeX3 in my
TeX-based work, and I'm trying to embed expl3 code in commands created
resorting to the xparse facilities. This is where my trouble starts. Well,
maybe this particular issue is not related at all with xparse but with
LaTeX3 Booleans, or expansion, or whatever...
Banter enough. This is a small snippet from a real-life working project
(not pretending by any means that what follows is good LaTeX3/expl3
practice):
\documentclass{memoir}
\usepackage{xparse,l3keys2e}
\ExplSyntaxOn
\cs_generate_variant:Nn \bool_new:N {c}
\cs_generate_variant:Nn \bool_if:NTF {cTF}
\cs_generate_variant:Nn \bool_set_true:N {c}
\tl_const:Nn \c_prefix_tl {g_amod}
\tl_const:Nn \c_postfix_tl {_bool}
% Booleans making
\NewDocumentCommand\MakeBool { m }
{
\bool_new:c
{ \tl_use:N \c_prefix_tl { #1 } \tl_use:N \c_postfix_tl }
}
% Setting Booleans to True
\NewDocumentCommand\SetTBool { m }
{
\bool_set_true:c
{ \tl_use:N \c_prefix_tl { #1 } \tl_use:N \c_postfix_tl }
}
% Typing Boolean value
\NewDocumentCommand\ShowValBool { m }
{
\bool_if:cTF
{ \tl_use:N \c_prefix_tl { #1 } \tl_use:N \c_postfix_tl }
{ true } { false }
}
\MakeBool{columns} % Create a Boolean \g_amod_columns_bool
% l3keys defining and setting
\keys_define:nn { amod }
{
columns .bool_set:N = \g_amod_columns_bool
}
\NewDocumentCommand\DocumentSetup { +m }
{ \keys_set:nn { amod } {#1} }
\AtBeginDocument{%
\DocumentSetup{ columns = false }
}
\begin{document}
\ShowValBool { columns }% False from l3keys
\par
\SetTBool { columns }% set to True
\ShowValBool { columns }% True from above command
\par % Yes, what comes is ugly enough, but just to check...
\bool_if:cTF% raw expl3 code to check Boolean value. Should return True
{ g_amod_columns_bool }
{ True } { False }
\end{document}
% And, for a terrible ending...
\ExplSyntaxOff
The problem is that I'm gettting False True False, whereas I would expect
False True True. What is going on here? What is it that I'm missing or
skipping?