I attended elementary school in HISD and middle/high in SBISD. The article doesn't quite get to the root of the issue. The issue is that the programs tend to be targeted towards long time residents with a lot of cultural and political capital. These are the people that can make or break the career of a school administrator, so they get deference. This can happen because information about the programs are not publicized much. It's also expensive to run GT programs and the system doesn't want too many kids qualifying. As a result, the kids who end up in GT programs are those whose parents know all about the program (from knowing other parents with kids in the program) and have the wherewithal to lobby teachers to recommend their kids for testing and advocate that the kid get put in the appropriate program.
To illustrate how this works: my parents were not from Houston, but settled in the town shortly before I was born. They knew to get me tested, and I scored at a level that qualified me for any of HISD's gifted programs. However, what my parents were not told (and what could not easily be found out in a pre-internet age), was that there were actually multiple levels of gifted program. While I qualified for the higher tier program, nobody told my parents about it, and I ended up in the lower-tier program by default. My local school wanted it that way because I was a guaranteed pass on state standardized tests and the higher-tier program would have involved a transfer to a gifted magnet school. By the time my parents figured it out, we were moving to a nearby district that had a completely different system.
As far as the test being biased, it may be, but only to the extent IQ tests are biased. As far as I know, they are still using a version of an IQ test for selection, with certain additional diversity points available for kids on the margin. For a young child, providing some familiarity with the test could be helpful, so there's probably some benefit to savvy parents prepping. But I doubt any tweaks to testing procedures would make up for the cultural capital factor.