I just realized the Phoenix Area Turf Report includes some other information that can be used to derive their water use numbers (see remainder of the June 16 report below):
Multiplying 2.13 (ETos for the last 7 days) times 0.73 (acceptable crop coefficient for Bermuda), we get the 7-day average watering recommendation, 1.55". Similarly, 2.13 * 0.83 (high crop coefficient) = 1.77", which also matches the report.
We can solve for the analogous ETos Rachio must have used from June 10-16. Since I entered a crop coefficient of 0.78, this implies Rachio must have used 2.26" / 0.78 = 2.90, which seems rather high. For June 16, it would have been 0.33" / 0.78 = 0.42, which is higher than all of the areas given in the turf report. I'm not sure how Rachio is coming up with ETos from the weather reports (KIWA or KCHD), but it seems like the method used must be different than what was done in the Phoenix Area Turf Report.