There is a reason that the original wording for feats/features like this was "You know the [x] spell, and can cast it once at [base level] without spending a spell slot". This wording is specific and non-frivolous: You know the spell. that is not fluff. You know the spell; you can cast spells you know using your spell slots. This is covered in the magic rules and re-covered from the other direction in the multiclassing rules.
It wasn't explicitly stated because it didn't need to be, and 5e design standards (at least when it was first devised and released) are to say exactly what needs to be said, and that things do as they say and not what they don't. when a feature tells you that you know a spell, it doesn't actually need to say that you can cast that spell using spell slots; it's baked into the spellcasting rules.
Unfortunately, in the more recent books, they've back-tracked on this principle and started to explicitly re-state elements, which in turn has had the undesired effect of causing people to think that the earlier features don't allow this; that is not (intended to be) the case.
