"High Availability" -- it is exactly what it sounds like. If your networking frequently has problems, and the database server is unavailable, then it should not be labeled as "Business Critical" nor as a HA offering.
I understand that you are saying a networking issue does not mean the database is down, but if the database is unreachable, then it doesn't matter that the database itself is still running on the physical node. If the database cannot be reached, then for all intents & purposes, it is considered down for your clients, period.
I've emailed the address you suggested but if the understanding by Microsoft is that Azure DB for MySQL can be running but not accessible via any network, and that qualifies as Highly Available... well you can come to your own conclusions.