Nobody is talking about spell slots.
Wrong -- everybody is talking about spell slots. The entire point of the 'as a single classed caster' argument is that the clause supposedly directs you to refer to the class chart to see what spell slots a caster of that level would have, which then limits the level of spell that class can prepare. The thing is, 'as a single-classed caster' isn't the same as 'use your class level to determine your spell slots for the purpose of preparing spells'. This is even more true when you realize that class level is the limiting factor in determining how many spells you can prepare, and the rule about using your single-class level to determine what spells a character can "know and prepare" can be interpreted as referring only to that requirement, not to how to determine what spell slots a multi-class caster has available (which as noted has its own multi-paragraph entry in the multi-classing rules).
Not only is this claim unverifiable, it is also irrelevant. Since when do anonymous DMs in the AL have rules interpretation authority?
Since it's listed in the Adventurers League Player's Guide: "A DM's ruling at the table is considered final for the purpose of that play session." An Adventurers League DM can even overrule Jeremy Crawford; campaign administrators have repeatedly said that Sage Advice is not official for Adventurers League (though it can be used if the DM chooses to).
No, you could play with ten different DMs and get ten different rulings. And that's a good thing - but also makes them a completely inappropriate source to discuss RAW.
At the risk of taking this thread entirely off-topic, there is no RAW -- every rule is interpreted. Some rules are easily interpreted and nearly everyone comes to the same interpretation, others are vague and subject to different interpretations, but all rules are interpreted. RAW does not exist.
I suggest you focus on the matter at hand.
Sure.
To begin with, the example under multiclassing doesn't mean what people seem to think it means. A lot of people are focusing on the phrase "know and prepare"; the reality is that no spellcaster (with the possible exception of the wizard, but see below) both 'knows' and 'prepares' spells.
The example Ranger4/Wizard3 correctly knows 3 1st level ranger spells, because the rules for the ranger specify that it's your ranger level that determines what spells you know based on the Ranger level chart. The example doesn't note what spells the Ranger prepares, though, because classes with a 'spells known' list don't have a prepared spell list -- their list of spells known is their list of spells prepared. Likewise the Wizard example correctly notes that the Wizard may have two 2nd level spells in his spellbook for free, since the rules for gaining free spells when you go up a level in Wizard specifically note that you gain free spells for which you have spell slots "as shown on the Wizard table". These are explicit call-outs in the rules for the individual spellcasting classes, and apply whether a character is single-classed or multi-classed.
Here's the wrinkle -- the example doesn't explain that the Ranger/Wizard could prepare a 3rd level wizard spell if he happened to have one in his book. That's because this is a corner-case that won't always apply, and it's not worth pointing out every corner-case in a generic example. But it is possible: the rules for spellbooks say that a Wizard can copy "a wizard spell of 1st level or higher" into his spellbook "if it is of a spell level you can prepare". The rules for preparing wizard spells say that a wizard can prepare a spell "from your spellbook" of "a level for which you have spell slots." That's it; unlike the rules for adding free spells to your spellbook, the rules for preparing spells do not specify that you use the Wizard class chart to determine your spell slots. The requirement that the spell be in the spellbook clearly doesn't apply when considering whether or not the Wizard can put a new spell into his spellbook; if it did, then the entire "Copying a Spell into the Book" section of the "Your Spellbook" sidebar would be meaningless. So the only restriction on adding spells to the spellbook is if the character has the appropriate level of spell slot. A Ranger4/Wizard3 casts as a 5th level caster (3 levels of Wizard, plus half his 4 levels of Ranger), and thus has a 3rd level spell slot. If this example Wizard can find a scroll or other spellbook with a 3rd level wizard spell, he can copy it into his spellbook, since he has 3rd level spell slots. Once the spell is in his spellbook, he can prepare it.
Once you have that, it's an easy step to saying that a Wizard19/Cleric1, who has 9th level spell slots, can prepare 9th level cleric spells (as well as 9th level wizard spells in his spellbook). A Cleric19/Wizard1 could prepare 9th level wizard spells, if he managed to get any in his book.
The other key point here is that the requirement that characters determine their spells prepared or spells known as if they were single-classed casters does not mean you ignore the rules for how to determine how a multi-classed caster determines his spell slots; that would be like saying that the rules for preparing spells as a Wizard use the same text as the rules for gaining free spells when you go up a level. But they don't; that's an oversimplification of the rules in the book.
Wouldn't you say that your interpretation is the preposterous one? If I understand you correctly, you're arguing that a single level of a spellcasting class gives access to all spells of that class, provided you have enough levels of another spellcasting class to actually cast them?
Of course not -- not every spellcasting class has access to all the spells on their spell list. Bards and rangers have a 'spells known' list that is necessarily limited and has to be based on their class level to make sense. Warlocks have an entirely different method for determining their spell slots, both as a single-class and as a multi-class caster. Paladins have access to their full spell list, but since they are a 'half-level' caster class, a Cleric1/Paladin19 would not have access to 9th level cleric spells, since such a caster doesn't have 9th level spell slots. There are really only a few class combinations that allow 9th level spell access for both classes, and in some cases, like the Wizard, there are additional restrictions that make some combinations (such as Cleric19/Wizard1) much more reliant on player initiative to get access to the appropriate spells. By no means is this a ruling that says 'everyone gets 9th level spells!'
Of course, if you want to claim that to try to defeat my argument even though I'm not saying that, because no better argument seems to be available to you, go ahead. I trust that intelligent players and DMs will see the distinction between the two arguments and choose appropriately.
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Pauper