No, he is not incorrect. The government code, in 411 (h), does not set out offenses. The penal code does. 46.02 makes it unlawful to carry a handgun, illegal knife or club, with certain exceptions. PC 46.15 (b) states, in part, that 46.02 does not apply to a person who is carrying a concealed handgun (at least for 9 more days) AND a valid license. That section does not restrict the non-applicability to to only the carry of handguns.
Well, in my LexisNexis, it appears to...
"PC 46.15 (b) Section 46.02 does not apply to a person who:
(6) is carrying a concealed handgun and a valid license issued under Subchapter H, Chapter 411, Government Code, to carry a concealed handgun;
Check out PC 46.15 (c), (d), (f) and (g)