Blast from the past here

- hope this is ok...I'm a recent convert to AmEx and have their platinum card, trying to make the most of all the offers and benefits they provide. The AmexTravel site appears to be a wildly different beast than when it was last discussed in the forum here, with a ton of hotels available, and also a separate faceted search for filtering on FHR and/or THC properties.
I'm noticing that almost every rate for properties I'm going to be staying at later this year
exactly match the Hyatt standard rate when I look at their website for a direct booking.
That said...if I book through AmEx Travel for a Hyatt property, and the rate matches what's on the Hyatt.com website...will I get my base points? Prices are identical, and when I'm looking at the Hyatt Terms and Conditions for points they only talk about eligible rates these days...just want to be sure I'm on the right path, and hopefully able to double-dip the MR points and Hyatt base points as well. Maybe someday I can make it to be a lifetime Globalist ¯\_(ツ)_/¯