Well, they degrade in sea water better than plastic so they're better for sea life. So the null hypothesis that plastic bags and paper bags are the same for sea life is easy to reject because the evidence is easy to collect.
For them to then be not any better in overall impact, it must mean you have some evidence that rejects the null hypothesis that plastic bags and paper bags are at least identical for all other purposes. So let's see it.
I know it's a surprising result, but this is a well studied topic, so there actually is a lot of evidence out there, and the scientific consensus seems to indicate that paper bags have a much higher impact than you might expect. You should plan to reuse a paper bag three to four times as often as a plastic bag to even out the impact.
Total impact analysis can often be really counterintuitive.
EDIT: Was trying to answer the question asked in as polite a way as possible, with links demonstrating the scientific consensus. Sorry if I offended someone?
These are all GHG results not an "overall for the environment" result. GHGs are only one part of the equation. I buy TerraPass, for instance, so the GHG part is going to be offset one way or the other. But if I were to buy plastic I'd be negative carbon but still killing sea creatures.
Hmm, fair enough. In either case, though, I suppose it's fair to conclude that the original statement I was responding to is correct about overall costs (i.e. it is not, in fact, clear)
FWIW though, I think it might still be the right decision to go paper over plastic because of the accidental risk. I can't really control all downstream uses of my plastic bag once it's in the bin.
For them to then be not any better in overall impact, it must mean you have some evidence that rejects the null hypothesis that plastic bags and paper bags are at least identical for all other purposes. So let's see it.