It seems that using mined virgin oil for plastics that gets tossed in a landfill means that at least a little more of the oil we are mining ends up not getting burned and emitted as CO2. In this way, we're creating non-global warming demand for oil which competes with the energy demand in the market. I don't know if this is a reasonable way of thinking about it.
Of course, the energy required to haul a bottle of water hundreds of miles is huge, so I'm not arguing for buying more plastic waste, just not sure how recycling existing plastic waste affects global warming in particular.