Does storing meat in plastic alter how long it takes to go off?
The question is 'plastic vs. what else?'

I admit I've never done side-by side tests to prove it, but from my observations, when the deli I went to switched from butcher paper to zip-top plastic bags, sliced lunchmeats wouldn't last in the fridge as long.  They'd start getting slimy around two weeks.**

I've noticed the same thing (although longer time frames) with firm and hard cheeses, and my solution for those has been to wrap the cheese in a paper towel, then put it back in the plastic bag.

I suspect that the issue is moisture buildup (you open the packet, let in cold air, it condenses in the freezer, etc.), and if this is the case, then other non-porous materials (glass, metal), would be equally bad for storage, especially as you can't then squeeze them to remove the air.  The butcher paper always stays at roughtly the size of the item being wrapped.

... but still, even if we did experiments, to say it's always bad, we'd have to also test raw meats, ground and whole (and for moisture, many stores put those little diaper pads in the containers), tightly vs. loosely wrapped, and a few other variables.

** Some health person is going to complain 'but you're not supposed to keep meat in the fridge for 2 weeks ... this was well preserved items like sweet bologna)