This doesn't sound credible, and I can't find a source for this claim. Not all residents have cars (ie, many residents are children), so the number of parking spaces per car would be around 40. This necessarily implies that at any given time only 2.5% of the parking spaces in the city are occupied. That doesn't pass the smell test.
When accounting for driving lanes, a parking lot has around 1 space per 300 square feet. At 30 parking spaces per resident, that would mean Houston would have a square mile of parking lot for every 3100 residents. That also doesn't pass the smell test, as the amount of parking within the city limits would be greater than its total land area. I've never been to Houston, but I can't imagine there's enough structured parking there to pull off that feat while still having room for roads and buildings.