Hi and Welcome to the Texas Forum. If he's in for a case that he's already got an approved court Attorney for...I would assume he could keep this attorney. You can always retain a New Attorney. If you obtain a new Attorney, inform the New Attorney of the Court Appointed Attorney and he will notify him/her of this matter.
I'm wondering if you're referring to a rumor I also heard - that there are some Harris County judges who have the feeling that IF you're able to bond out you can afford your own attorney. I've heard that rumor but in all my years dealing with Harris County I've never heard a judge in the court room say it.
I have, however, been in the court room during roll call where the accused is sitting having been released on bond who - when asked by the judge if they have a attorney - has answered no. They were then given a reset for time to obtain an attorney or a court appointed was available.
To the best of my knowledge you are not obligated to keep the court appointed if you prefer to hire your own.
Hope this helps. Best of luck!
__________________
"We can rejoice, too, when we run into problems and trials, for we know that they help us develop endurance. And endurance develops strength of character, and character strengthens our confident hope of salvation" Romans 5:3-4