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I'm going to share a sentence my father blew my mind with when I was 16:
"Unreliability is the internet's biggest, best feature."
By this, he meant that the internet is extremely fail tolerant; one server, one site, one component goes down, the rest of it keeps working.
I think that's at play here. An instance can keep up with its own local members and subscribers, I imagine that's just a database operation, MySQL or something. But when trying to total up total number of subscribers from other instances, very realistic problems start to pop up.
A member from Instance A subscribes to a community on Instance B. How does Instance B keep up with that subscription? A sends B a message that someone has subscribed, so it adds an entry to a "foreign subscribers" list? Cool. And I suppose an "unsubscribe" message would also be sent to remove that entry, right?
What if that user deletes their account or it's banned? What if Instance A just...shuts down one day and never boots back up? You'll end up with these ghost entries inflating numbers. It's not an easy problem to work around.
At a high level you've pretty much nailed what is happening.
Lemmy federates these to let other instances know. Check the mod log (link at bottom of every lemmy instance website) to see the record of this.
This is already an issue, but a solvable one. Currently some instances are blocking hundreds of other instances that used to exist but no longer do, because Lemmy keeps trying to contact them and when it fails it retries. It's causing instances big performance issues.
But the solution probably isn't that hard. Someone smarter than me can work it out but I imagine it working something like retry every 5 mins for an hour, every hour for a week, then don't retry until you get a new request from that instance (e.g. for one of their users to subscribe to a community on your instance).
In fact, Mastodon is a lot more mature than Lemmy and I expect would have the same problem, so we can probably copy whatever their solution is.