I'm not convinced by your arguments:
the circle says you can summon the creature in it's zone, and the reanimated creature is summoned (whatever spell you use).
the only problem is that when you reanimate (whatever spell you use) it's not clearly YOU who summon (the creature "is summoned").
Note that, unless it says otherwise, the Mage who controls the effect which grants Reanimation is the object summoning the creature into play.
There's a lot here that seems unclear to people, but this shouldn't be. The mage is definitely the object doing the summoning when they reanimate a creature. I also recommend reading the Supplement regarding Reanimate as it has a little more detail on the whole process.
To the initial question, RAW I agree with Puddinhead. Precise wording matters. Summoning Circle says explicitly that your Mage may choose to summon the creature to Summoning Circle's zone
INSTEAD OF their own zone. The card only says it's able to redirect from the Mage's zone, not from elsewhere, and we can't give it powers it doesn't have.
That does mean it has some weird wiggle room though, which I'm not really a fan of. Technically it then CAN work with Reanimate effects, so long as the zone that the creature is getting reanimated into is also where the controlling mage is at. I don't really understand why that should matter, but as written that is how it would work. It then fulfills all of the requirements of Summoning Circle. Your mage is summoning it. Check. It is a friendly creature. Check. It is being redirected from your mages zone to the Summoning Circle. Check. Summoning circle doesn't care about the restrictions that other spells have, or the fact that they could have been outside of the Mage's own zone. What matters is where they were actually going to be summoned to. I'm not sure why that matters, but RAW it does. We can argue RAI till we're blue in the face.
Hopefully this answer equally disappoints/upsets everyone, lol.