Can an Arcane Trickster or Eldritch Knight who takes the Magic Initiate? [duplicate]

Can an Arcane Trickster or Eldritch Knight who takes the Magic Initiate (Wizard) feat cast the first level spell they pick with their spell slots, like a Bard who took Magic Initiate (Bard) can? Or the Wizard for that matter?

Both AT and EK uses the wizard spell list, so one could assume so, but can they?

This question have not been directly answered when it comes to Arcane Trickster or Eldritch Knight, so please do not close my question, the problem is if it counts for AT and EK.

I repeat, this specifik question needs to be clearly answered 🙂