@jbethany Ah ha! I think we are onto something here! I used provenance to figure out what even sampling depth you used when running core-metrics:
[note: this screenshot came from loading bray_curtis_pcoa_results.qza at https://view.qiime2.org and navigating to the "Provenance Tab"]
Then I generated a summarize viz for your filtered table, and plugged in that even sampling depth (32150):
[note: this screenshot came from running feature-table summarize]
As you can see, at this depth, you filtered out all but 4 of your samples: TI3, TI5, FF21, and TI4, which means the rarefied table used to compute the distance matrix only had 4 samples in it, instead of 36, like you expected.
This means that, effectively, the only metadata values that are actually being used are:
[note: this screenshot came from running metadata tabulate]
So the error you saw before makes sense, because you are attempting to perform a pairwise comparison (--pairwise) to all of the "groups" within the category Site, but two of the three "groups" (coldsiltfinal1 & hotsiltyinitial) only have a single value within them, so there is no way to compute the "within" distances (there is nothing to compare to!)
So specifically, you can drop the --pairwise parameter, and then it should work for you, but, I suggest that you take a step back and rethink your rarefaction depth, since that is some pretty aggressive filtering, and was responsible for some unexpected behavior here.
Hope that helps! Thanks! 
