Where does the bash PATH on CentOS 7 get /usr/local/bin from?

In the bash source "config-top.h" has this:

/* The default value of the PATH variable. */
#ifndef DEFAULT_PATH_VALUE
#define DEFAULT_PATH_VALUE \
  "/usr/local/bin:/usr/local/sbin:/usr/bin:/usr/sbin:/bin:/sbin:."
#endif

/* The value for PATH when invoking `command -p'.  This is only used when
   the Posix.2 confstr () function, or CS_PATH define are not present. */
#ifndef STANDARD_UTILS_PATH
#define STANDARD_UTILS_PATH \
  "/bin:/usr/bin:/sbin:/usr/sbin:/etc:/usr/etc"
#endif

Other people have asked the same thing on the CentOS bug tracker. The earliest post I found was this one.

/usr/local/bin is hardcoded in /bin/bash.

1. https://bugs.centos.org/view.php?id=10200
2. https://bugs.centos.org/view.php?id=10199
3. https://bugs.centos.org/view.php?id=10198
4. https://bugs.centos.org/view.php?id=7492

As you will see this problem was first reported in May 2012, and has existed in CentOS 6 and CentOS 7.

So as confusing as it may be, it looks like your analysis the paths are not coming from /etc/profile is correct. The paths are coming from /bin/bash.

It definitely looks hard coded into /bin/bash

strings /bin/bash | grep "\/usr\/local\/bin"
/usr/local/bin:/bin:/usr/bin

which seems to be the default PATH.