It seems there is a bug with both the UI and the mgmt API when it incorrectly invalidates the "destination".
It expects a 32-character string (which is OK), but then there must be further buggy validation rules that results in a 400-error when you attempt to use a valid PagerDuty Integration Key.
The error on the UI is; "Please match the requested format"
The error via the management API is;
{"errorCode":9,"status":400,"message":"Unsuccessful request: https://apigeenotifier.googleapis.com/v1/organizations/apac-syd-partner7/subscriptions/1284333d-6f13..., ResponseCode = 400\n"}
I have found the answer - effectively I was using the wrong "Integration Key" from PagerDuty.
Using the correct Integration Key
On the PagerDuty UI;
Use that Integration Key in your Alert Rule Destination.
For those interested in the WRONG way see below;
There is also an Integration Key under the Configuration > Event Rules section. When you create a new Event Rule, you also get an Integration Key (but this time it's all upper-case). This is not the right key and won't be accepted by Apigee.
@David Freeman- thanks for contributing an answer to your own question! That helps everyone.
@Will Witman - maybe this is worth flagging in the docs?