Being pedantic - this is a policy decision for each Organisation to make and agree with their stakeholders.
In my previous life, we determined that a "meaningful" response was required, and defined that as being a human interaction - phone call, face-to-face, or email but excluding any automated "Your request has been accepted/assigned" etc. interactions.
If I remember correctly we stipulated that any non-email first response had to be followed up with an email summarising the interaction so we had a concrete record (for other reasons than progressing the Request) but that meant we never faced the "whichever comes first" scenario.
Based on your last reply, a Human Task with an "I responded via email/phone/visit/other" option would work, but I appreciate that might be viewed as an extra click by the analysts.