I doubt this net-loss is the case for most new gas fireplaces with direct-vent exhaust systems, in which case the combustion air comes from the outside. This is what I have. Not sure how common these would be in Texas. It can also be used in the event of a power outage. (Minus the fan) [1]

[1] https://www.heatilator.com/owner-support/troubleshooting-and...