The solar exaltations that the infernal ones are made from were themselves made by a god and infused with his essence and nature.
They were made by a Primordial, blessed/infused by a god, them blessed/reinfused by another set of Primordials.
Do keep in mind he is an elemental, and elementals are inherently servants to exalted. it in their nature as elementals.
1)This is not accurate.
In 2E the Elemental Courts were created by the Primordials to help regulate Creation's natural processes.
Celestial Exalts have some authority over them as part of the overthrow of the Primordials, but its supposed to be strictly regulated.
You get to borrow them, but they still have their own jobs to do.
2)Even if it was true, Infernals would have no authority over elementals of Creation.
Because when your allegiance is to Malfeas/Hell, you cant claim authority over elementals whose chain of command terminates in Yu-Shan/Heaven.
Do note that "who we all work for" is explicitly the thing Lydia is asking for, and isn't going to* explain shit without knowing.
*doesn't currently intend to, at least. I'm sure there's social-fu that could change that, although I'm not sure we'd like the aftermath of e.g. intimidating it out of her.
Dont mistake teenage dramatics for any sort of coherent policy. Meet her halfway and she'll fold.
She literally has no way of confirming anything she's asking us to tell her here. We could tell her any manner of baldfaced lies about our allegiances and she wouldnt be able to tell the difference because she apparently got fuckall supernatural education and has no magical lie detection. Imagine being a supernatural in Chicago for almost a year and not knowing who Michael Carpenter is.
Look at the poor girl's situation.
Her father, in an apparent attempt to raise her normal, left her with so few supernatural references and sources of information that she got conned into letting a disembodied necromancer almost eat her alive. She has only been in Chicago for less than a year, so she has no community links, and was sheltered before that.
She has no way of physically compelling her will against three armed combatants.
She cant go back home because she let the Capriocorpus inside the wards, and she has no way of checking if it will come back. The bodyguards she's previously mentioned are mysteriously absent.
Girl is just attempting to reassert some control in her life after profound trauma by saying Papers Please.
Its not a serious attempt at identification, its a plea for reassurance.
Note that she isnt scrambling for her phone to call her parent for help, like most teenagers would after something tried to kidnap and eat them. Which means either her father doesnt have a cellphone, which is possible but unlikely even for an oldfashioned person, or he's missing, and she knows calling his phone wont reach him.