Sure, batteries don't last forever. It does make perfect sense to consider the environmental costs of batteries. The comparison should be made considering also the costs in time and diverted resources of money and teams of uber-smart engineers to a technology that will not be deployed on a large scale anywhere near as quickly as BEVs could be, when replacing the fossil fuel infrastructure should be a top priority. Fuel cell vehicles on a small scale are irrelevant. On a large scale, they'll create more short-term demand for hydrogen, which in the real world would come almost entirely from fossil fuel sources.
I'd guess Romm quotes Cox because he thinks Cox summed up the case well. Perhaps Cox is a sleazy businessman with a conflict of interest, but the analysis checks out. Certainly all the uber-smart engineers working on hydrogen have as much skin in the game as someone making lithium batteries.
It's certainly well-known that BEVs today use all kinds of "dirty" energy. So would fuel cell vehicles if they existed at a scale that represented a significant portion of transport.
An apples-to-apples comparison could involve BEVs with clean electricity against fuel cell vehicles with clean energy; BEVs are superior on efficiency. Another could involve comparing BEVs with today's electricity sources with fuel cell vehicles using today's hydrogen sources. Exactly how well BEVs fare depends on where you're charging them, but in this case, they still outstrip fuel cell vehicles not yet available on any significant scale - and the latter, with their support infrastructure yet to be built, still don't outperform available technology like gas-powered hybrids.
A skewed comparison pits BEVs powered with a crappy fuel mix against fuel cell vehicles powered fueled by solar panels and sewage. That's the one comparison fuel cell vehicles win consistently, and its the one you seem to insist upon. But it's intrinsically slanted because BEVs could use the same energy sources.