Not necessarily. If the stem is spongy or slimy, then it's rotting, but that looks like it's hard and brittle. Still, though, it's likely that that stem won't be as healthy as the others. Why not just cut it off anyway, and give the other three some more room?

I would also consider pulling that mulch back from the stems a bit, to lower the humidity around the crowns.

Agree with Sophie's comments.

Thank you--I'll harvest that stem! It wasn't slimy or soft yesterday.

Any thoughts as to the cause? I have seen quite a few earwigs around, some inside my strawberry hanging planters. I'm in a very challenging climate for basil--in the foggy, western part of San Francisco, so there's plenty of damp, wind, and little warmth/sun for long stretches. But they are clearly growing and looked good other than these brown patches. I think the second plant also has some damage, but much less, similar to the stem in the back right of my pix. Thanks for your help!

Try removing the mulch to make a less hospitable environment for earwigs. What is 5-1-1?

5-1-1 is a mix that is hugely popular on the Container and Citrus (and maybe other) forums. It is a very fast draining mix. There are a million discussions, testimonials, and debates on the Container forum if you are interested in knowing more about it. GardenWeb member Al/Tapla is the father of the 5-1-1 mix and its big sister, the gritty mix, which is also used by many here. (These aren't commercial pre-made mixes--they are formulas, which can be tweaked and adapted, for build-your-own media.)