I tried to start up the Notification Services instance and got a 1359 error:
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Services
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Could not start the NSxxxx service on Local Computer.
Error 1359: An internal error occurred.
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OK
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Inspecting the error log, I found this:
Description:
The Notification Services instance encountered an error in one of its components and must stop.
EventParameters:
Instance Name: xxxxx
Problem Description: The database was created with or upgraded to a different edition of Notification Services. Use the Notification Services edition that the database expects.
Notification Services Edition: Standard Edition
Database Edition: Enterprise Edition
So it turns out that the consultant was partially correct - Notification Services won't start if the version is mismatched between the engine installation and its corresponding SQL Server instance. Good to know.