If black mold is discovered underneath the siding, does that necessarily imply interior air quality problems?
Older homes without vapor barriers may not necessarily have black mold problems, but they probably do not have very good insulation or air conditioning either.

Houston, TX is a humid subtropical climate with average summer conditions of 95 degrees F and 75% humidity, so lack of a vapor barrier on the outside walls of this new home will lead to IAQ mold problems inside if other conditions are correct.

The dew point for 95F air at 75% RH is about 85F.  Without the vapor barrier, hot humid outside air in summer will likely make contact with internal surfaces cooled below 85F by the A/C, causing condensation well inside the wall.  The better insulated the wall is inside, the farther in the condensation will occur, since the dew point will move toward the direction of the insulation.  During summer the exterior wall without the barrier could be wet internally, not just underneath the siding (depending on indoor and outdoor conditions and how the insulation is constructed within the wall).

It might be possible to mitigate this somewhat by making certain the A/C system creates positive static pressure within the house; however, if the A/C system causes negative static pressure in the house, then the problem will be especially bad.  I suspect that is how this guy in New Orleans got into trouble: How to solve new condensation in bathroom exhaust fan ducts?

The following link points to a helpful essay titled, "How to Avoid Moisture Damage to Walls from Condensation":  http://www.tlpca.org/images/articles_condensation.pdf   See the description on page 9 for damage that occurs to a Florida home when there is not a vapor barrier on the outside and vinyl wall covering is installed on the inside.