This is the very point I'm debating.
Its the order of operations that you're taking which is the issue. You're saying that 1st-level wizards cannot prepare anything other than 1st-level spells because the wizard is first level but no such restrictions exist. The wizard can prepare any spell regardless of level as long as they have the spell slot for it. Its just that single-classed wizards would usually only have 1st-level spells.
If a magic item granted this 1st-level wizard a second-level spell slot, the wizard would be able to prepare a second-level spell because he has the slot for it.
Going by the letter of the law, so to speak, you could possibly make a case for a
Single classed wizard who has his spell slots somehow artificially increased being able to scribe and prepare a spell that is normally higher than his ability to cast.
This, to my mind, would be contrary to the spirit of the rules and I personally wouldn't allow it, but if in your game you see it as logical then all the power to you.
To that end, by the letter of the rules, a multiclass wizard would still be barred from preparing and scribing spells higher than they can cast as a single class, even if they have a higher level spell slot. This restriction is clearly defined.
A wizard can only prepare wizard spells they have in their spell book. (PHB pg 114)
A wizard can only scribe spells into their book if it is of a level they can prepare. (PHB pg 114)
You prepare spells for each class
individually as if you were single classed. (PHB pg 164) - which suggests that in calculating what you can prepare you would compare your spell slots of a single classed character NOT a multiclassed character. A single classed 1st level wizard has 2 first level spell slots. You don't count your actual final spell slot availability based on multiclassing for determining what can be prepared. That's covered in the next section:
If you have
more than one spellcasting class, and you have spell slots of a higher level than you can
normally prepare, you can use those slots
but only to cast your lower level spells (PHB pg 164) - this line in particular is a very clear restriction as to what the slots can be used for.