Does Magical Training allow you to take Precocious Apprentice?

[Doctor Awkward]

You didn't really answer the question though. What other purpose does your arcane caster level serve such that the line you quoted is making a meaningful difference from the norm?

I didn't answer your question directly because it's irrelevant. In order to take Precocious Apprentice you are required to have an arcane caster level. Arcane caster levels come from having levels in an arcane spellcasting class. Exceptions to this, like everything else, must be specifically called out as such. An all encompassing set of the different functions a caster level might serve is a meaningless line of inquiry given the subject at hand.

You cast them as a wizard/sorcerer. This makes them arcane spells. The caster level of your spells is equal to your arcane spellcaster level which is a minimum of 1.

Yes. You are given explicit permission to cast them just like the thing that are not. This is an exception to the normal rule that only characters with levels in the appropriate spellcasting class can cast these spells. Every other benefit that you get from the feat is carefully and explicitly spelled out by the rules text because that's how exceptions work. If the feat simply said, "You have an arcane caster level of 1," then went on to describe what that meant then the feat would work as you want it to. But it doesn't say that. So you don't.

Magical training certainly satisfies the bolded.

...which would matter if Magical Training explicitly granted the character spell-like abilities. It does not. That is the context in which that paragraph of rules is discussing. Selectively quoting rules text out of context is not only an explicitly incorrect way of interpreting the rules, but it invariably causes more problems than it solves.

You have misread what caster level says in the PHB:



It says most characters. If, "It further states that your caster level is equal to your class level in the class that you are using to cast the spell," is true then the fact that you have an arcane spellcaster level which modifies the caster level of the spells means that you yourself have an arcane caster level as you cast as a wizard/sorcerer of 1st level.

You have misinterpreted what it says in the PHB. It says "most characters" determine their caster level by looking at their class level because the rules are well aware of the existence of things within the rules which modify your caster level in some way. In fact, that is the topic of the very next paragraph. This is why context is so important.