You have an interesting situation.
In general, yes you do look at the "all-included" rate, but then you have to deduct the taxes
and fees from both to get the final rates which will be compared against each other. So it's not just comparing the final rates.
In your particular case, I noticed:
1. SPG has 2 taxes - a service tax (ISS) of 5% and a room tax of USD$9
2. Expedia has only 1 tax - they don't state the amount and what it consists of but a simple calculation shows that it is 5% ie the service tax (ISS)
Using your rates of $82 for expedia and $87 for SPG:
a. Expedia: $82 less 5% = $78.09
b. SPG: $87 less $9 and then less 5% = $74.28
which is what the BRG agent quoted you.
Now, this is the fun part:
. by right, the BRG agent should have deducted 5% and $9 from the Expedia rate. That would have made it even lower than the SPG rate
. But they only deducted 5%
. I'm not sure if they are supposed to vet the OTA rates for missing fees etc which they appear to have done in this case - I've never personally encountered this sort of situation
Anyway, I would clarify with the hotel and Expedia, asking if the Expedia rate includes the Tourism Tax of USD$9. If you can get in writing that it IS included, then you can send that back to the BRG team and request that they review the claim.
However, I personally feel that the hotel and Expedia will tell you that you have to pay the $9/room/night at the front desk...
Good luck!