Not true. Charles Bronson's office must be putting out bad info. At present, TX recognizes a FL permit for non-FL residents. I keep a Florida CWL, even though I have a TX CHL and am a CHL Instructor, since it is staggered, expiration-wise, with my TX license, and DPS is sometimes slow processing renewals. If they or I screw up and my TX license expires, I'm still good with my FL license. I'll not be surprised to see things change, once the legiscritters and DPS realize they are losing some money this way.
As to alcohol/drug-related matters: If you have an A or B misdemeanor (DWI will be one or the other) conviction, it will be 5 years after the date of conviction (NOT after arrest) before you can apply for a TX CHL. If you have two drug or alcohol convictions within 10 years before the date of application, you'll be denied as well, as being "chemically dependant." FWIW, there is no law against drinking and carrying in Texas, but you can't carry while intoxicated. Under that law, the .08% BAC presumption is not used, but rather the PI definition, "Danger to oneself or others." Double-edged sword, that.