Does it really matter which Hyatt phone number we call?

Today I had to call in to cancel a reservation. (I was a few minutes past the cancellation deadline, the Hyatt website was deliberately obtuse about whether I'd have to pay a penalty, and didn't want to take a chance.)

While clicking through the screens to get to my reservation, at different points I was given:

to modify a Gold Passport reservation, please call 1-800-30-HYATT;
Reservation Assistance 1 888 591 1234;
Hyatt Gold Passport 1-800-228-3360;
and Hyatt Place 1-800-993-4751.

After the CSR had quickly taken care of my cancellation, when I got the standard "is there anything else?" I pointed out that I was a HGP Diamond and asked if calling the Diamond line was really any different. she responded "Uhhh, no, not really."

So now I'm assuming all these numbers they throw at us actually all lead to the same group of CSRs. Anyone have a different experience?