Hi kwilky
I met the exact same issue here.
Based on testing of different criteria, I found other issues as well.
1. If your matrix with more than 5 measures and no field value (measures only) and the measures involve more than 3 tables, the exporting underlying data won't work. Check the Chrome console I got this
Failed to load resource: the server responded with a status of 500 ()
POST https://wabi-australia-southeast-redirect.analysis.windows.net/export/xlsx 500
2. For the cases in point 1, once I added a field from any table into that matrix (not measure), the exporting underlying data will work. But the results are incorrect, the columns are randomly selected, sometimes all the columns from one table, or maybe only three columns returned and none of them is related to the measures. Really weird.