That’s not how bacteria multiply. There is horizontal gene-transfer, but that would be a very slim chance.
No ancient bacteria aren’t the problem, multi-resistant strains that have already evolved and are evolving in our clinics are the real problem, some bacteria that haven’t been an issue for quite some time, because our antibiotics simply killed them, have now developed resistances and are suddenly becoming deadly again.
E. Coli, Staphylococcus aureus and Salmonella, some of the most prevalent bacteria in humans are rapidly becoming multi-drug-resistant and resistant to desinfectants like chlorine. These superbugs already account for a shockingly high number of deaths in healthcare facilities and the situation is only getting worse as more and more countries use increasing amounts of antimicrobials, kickstarting microbial evolution into overdrive.