Your link specifically calls out New York City. I could not find anything related to concealed carry permits and bribery for Texas. This indicates a poor implementation of law/regulation.
This is because Texas is a shall issue state where generally, you apply, meet the specified requirements, get a background check, pay your fees and the state will issues you a permit. If you pass all the checks you get the permit, no other considerations are made.
New York is a may issue state which generally/usually means a local law enforcement official will make a judgment call. Some have a blanken no issue policy, others sometimes waive that blanket no issue policy if they can be persuaded.