It doesn't say that, however.
You can only do spell-things as if you were a single-class character. The spell slots you have access to are considered separately. I don't see why this is such a confusing thing.
Well, you have the issue of obtaining 9th level spells in your spellbook. But yes, what does happen? It's a fair question. I know how I'd run it in my game (you can't) but I am not so positive the rules were written that way.
I am quite certain that is what the rules are aiming at. Unless you can point to something explicitly saying otherwise, why kick up a fuss about a possible implication of an intentional intersecting of two separate sections that don't relate to each other?
This is what 5.5e says about multiclass spellcasting characters (after the table, obviously):
Spells Prepared. You determine what spells you can prepare for each class individually, as if you were a single-classed member of that class. If you are a level 4 Ranger / level 3 Sorcerer, for example, you can prepare five level 1 Ranger spells, and you can prepare six Sorcerer spells of level 1 or 2 (as well as four Sorcerer cantrips).
Each spell you prepare is associated with one of your classes, and you use the spellcasting ability of that class when you cast the spell.
Cantrips. If a cantrip of yours increases in power at higher levels, the increase is based on your total character level, not your level in a particular class, unless the spell says otherwise.
Spell Slots. You determine your available spell slots by adding together the following:
- All your levels in the Bard, Cleric, Druid, Sorcerer, and Wizard classes
- Half your levels (round up) in the Paladin and Ranger classes
- One third of your Fighter or Rogue levels (round down) if you have the Eldritch Knight or Arcane Trickster subclass.
Then look up this total level in the Level column of the Multiclass Spellcaster table. You use the slots for that level to cast spells of an appropriate level from any class whose Spellcasting feature you have.
This table might give you spell slots of a higher level than the spells you prepare. You can use those slots but only to cast your lower-level spells. If a lower-level spell that you cast, like burning hands, has an enhanced effect when cast at a higher level, you can use the enhanced effect as normal.
At no point does the word "choose" appear. Hence, you must be referring to a specific class's Spellcasting section for your use of the word "choose"; in this case, Wizard. But the rules are very clear about what to do with that: "Whenever you gain a Wizard level after 1, add two Wizard spells of your choice to your spellbook. Each of these spells must be of a level for which you have spell slots, as shown in the Wizard Features table. The spells are the culmination of arcane research you do regularly."
Per the rules stated above,
the only thing that makes any sense is that you choose those spells as if you were a single-classed Wizard. It even explicitly says that you base your choice on what the
Wizard class table says, NOT anything about any multiclass table.