There are a couple of problems in the metric file used for the extended symbols, mt2exa.tfm. A NEXTLARGER command points to an incorrect character and another one is missing.
So this is definitely a bug; please, report it to the maintainers of the MTPro package and remember to announce when the bug is solved by adding the information to your question.
Workaround
If you are on a Unix system, create a work directory, say ~/fixmt2; I assume a Bash shell.
cd ~/fixmt2
tftopl mt2exa > mt2exa.pl
nano mt2exa.pl
(use the editor you wish, instead of nano)
Find the string CHARACTER O 266 and change
(CHARACTER O 266
(CHARWD R 0.646)
(CHARHT R 0.6615)
)
into
(CHARACTER O 266
(CHARWD R 0.646)
(CHARHT R 0.6615)
(NEXTLARGER O 270)
)
In the next entry
(CHARACTER O 267
(CHARWD R 0.646)
(CHARHT R 0.6615)
(NEXTLARGER O 270)
)
change 270 into 271 to obtain
(CHARACTER O 267
(CHARWD R 0.646)
(CHARHT R 0.6615)
(NEXTLARGER O 271)
)
Save the file and exit the text editor. Now run the shell command
kpsewhich mt2exa.tfm
that will answer something like
/usr/local/texlive/2012/../texmf-local/fonts/tfm/pctex/mtpro2/mt2exa.tfm
Issue
sudo mv /usr/local/texlive/2012/../texmf-local/fonts/tfm/pctex/mtpro2/mt2exa.tfm{,~}
so as to save a copy of the old tfm file (use the location you get for the file). Then do
pltotf mt2exa
and
sudo mv mt2exa.tfm /usr/local/texlive/2012/../texmf-local/fonts/tfm/pctex/mtpro2/
Now, running your file through LaTeX should give

\ProvidesPackage{mtpro2} [2009/4/27 v2.3 MathTimePro II - added arc accents MathTimePro II - fixed rbrace problem with straightbraces and morphedbraces options– Andrew Swann Dec 18 '12 at 16:01.sty), but not in the metric file.:(– egreg Dec 18 '12 at 19:05