If we have a large supply of very cheap energy, say from fusion or feeding a black hole, then a CO2 to jet fuel to CO2 cycle can be considered the same kind of thing as charging and discharging a battery. And it would be similarly "net zero" for CO2.
I hope these misleading "turned into" style of headlines go away when energy input is required. Carbon + Hydrogen + Oxygen + energy + information can be "turned into" pretty much any organic substance.
I mean, until the reserves are depleted the energy is basically free, we just need to pump it up and refine it.
(Then again, solar power is basically "free", we just need to catch it and store it... so my 2nd paragraph is maybe kind of dumb.)
If you had the renewable energy surplus necessary to do it, you'd make as much liquid hydrocarbon as you could, and pump it back into the ground.
However, you are right in the sense that taking advantage of our current hydrocarbon distribution infrastructure would save capital costs versus switching to, e.g., an all-hydrogen or all-electric energy infrastructure. The trick is to get those hydrocarbons from non-fossil sources, which is a solved problem from a technical perspective but very much still unsolved from an economic perspective.