Using and bending the rules the way is best for your table is always ideal! But it’s not necessarily the way to grasp or explain the subsystem’s role in the game or what it represents.
The difference between a relationship and another NPC is strictly about how important to the PC’s story they are, and how reliably the player can reincorporate them into the story. It’s mostly about game and story-level things, not ability. The “ability” it represents is just how connected the PC is, not so much a skill rating as a rating about a fact of their social web. (Page 378: “[Circles] allows the players to abstract the process of discovering who their characters know in the game world.”) It need not have some relation to the PC’s ability to make friends and enemies.
Hence, the capacity for Circles to promote NPCs to Relationships isn’t about simming an ability to make friends and enemies so much as it is about promoting an NPC from “extra” to “recurring guest star” in the PC’s organically-emergent personal arc. It’s “who you know and who they know”, so-called “networking”: the ability to get a meeting with someone or acquire an introduction, not also the ability to capitalise on the connections and meetings. So, meeting only; mingling and making friends is for other skills. (Invoking the enmity clause or lack thereof doesn’t so much dictate first impressions as it determines whether the connection has negative baggage. Page 383 notes that the enmity clause need not create outright enemies, just those who have a negative disposition, possibly due to a circumstance or past slight that’s fixable. Notably, it’s not a first impression, it’s an existing impression.)
The ability rolled always has to match the Task, too. If a player wants to find the foreign village’s medicine man (Intent), how (Task) matters: “I’ve heard of him before by reputation” is a (kinda thin, but still) Task that fits Circles. If it’s “I know villages and can spot the kind of residence a medicine man would have”, that Task would be Village-wise.