Bogus value of variable BASH

[David Hunt]

Configuration Information [Automatically generated, do not change]:
Machine: x86_64
OS: linux-gnu
Compiler: gcc
Compilation CFLAGS:  -DPROGRAM='bash' -DCONF_HOSTTYPE='x86_64'
-DCONF_OSTYPE='linux-gnu' -DCONF_MACHTYPE='x86_64-pc-linux-gnu'
-DCONF_VENDOR='pc' -DLOCALEDIR='/usr/share/locale' -DPACKAGE='bash'
-DSHELL -DHAVE_CONFIG_H   -I.  -I../. -I.././include -I.././lib
-D_FORTIFY_SOURCE=2 -g -O2 -fstack-protector --param=ssp-buffer-size=4
-Wformat -Werror=format-security -Wall
uname output: Linux unknown 3.13.0-77-generic #121-Ubuntu SMP Wed Jan
20 10:50:42 UTC 2016 x86_64 x86_64 x86_64 GNU/Linux
Machine Type: x86_64-pc-linux-gnu

Bash Version: 4.3
Patch Level: 11
Release Status: release

Description:
        On my notebook running Ubuntu 14.04.3 LTS /bin/sh points to dash, not 
bash.
        To get sh behaviour from bash I use the command `exec -a sh /bin/bash'.
        When I do so bash sets BASH to /bin/sh, which it demonstrably is not.
        The situation:
                none@unknown:~$ ls -l /bin/bash /bin/sh
                -rwxr-xr-x 1 root root 1021112 Oct  7  2014 /bin/bash
                lrwxrwxrwx 1 root root       4 Feb 19  2014 /bin/sh -> dash

Repeat-By:
        The demonstration:
                none@unknown:~$ exec -a sh /bin/bash
                sh-4.3$ [ "$BASH" -ef "/proc/$$/exe" ] || declare -p BASH
                declare -- BASH="/bin/sh"

Fix:
        I'm clueless.