Sure! Saying that the parent’s “develop an proprietary UI and use Loki as backend” is a slippery slope to “user sees data that incorporates data served from Loki” which I am arguing could be interpreted as data that would require the developer to maintain a source repository for Loki under the AGPL.
I see now and yes the AGPL seems vague in that regard.
If it's anything like dynamic linking and GPL that could be considered okay even if it's not the intention of the licensee. Seems like the license should be more explicit about what "interacting with" entails.