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> 「 **私に甘えっぱなしだ** なんて、そんなこと気にしないで良いんだからね……？」- act spoiled "to"/depend on me
>
> だからあんたも、何かの間違いで **私に惚れたり** しないでよ？ どうせ面倒なことにしかならなそうだし - fall in love
> "towards" me?
>
> はい、魔力とは人の持つ **欲望に根ざす** もの - probably location に, Included this to make sure
>
> でも、こうして１分１秒迷っている間に、地上は **滅びに近づいています** 。probably movement/destination に, but
> not physically moving. Included this to make sure
>
> 勝負？ **私に勝てる** と思ってるの？」- a match? you think you can beat me? (gain victory
> to?/from? me)
>
> というかお前に出来て私に出来ないはずないし……」-if you could do it, there's no way i couldn't; see
> below

I noticed that the dictionary of japanese grammar says [An intransitive verb
can never take
に...](https://djtarchive.neocities.org/bunpou/full_day.html#%E3%8A%A6%E3%81%AB\(2\)).

When I read this rule when i just started learning i didn't think much of it,
but now that I've read a fair bit of stuff this rule just doesn't add up.

I dug a few sentences just for examples, but i actually can't find any
examples of a transitive only verb directly following 私に in this script, but
there are countless examples the where an intransitive verb is.

Particularly with the last sentence, I were to write, "if you could do it,
there's no way i couldn't", in Japanese, i probably wouldn't have thought to
use に.

Are there any formal explanations ? Thank you

edit:
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grammar particle-に
Noun+に and intransitive verbs clarification
That statement is part of "●Notes 2.", i.e., the rule you mentioned is about
～に in the sense of "for (the sake of) ～" used with any "verb used in the
Verbてあげる or Verbてくれる construction". For example, even though you can say 学校に行く
in isolation, you cannot say ×彼に学校に行ってあげた nor ×彼に学校に行ってくれた in the sense of
"for him" because 行く is an intransitive verb. Instead, you have to say
彼のために学校に行ってあげた/くれた. By contrast, 彼に学校に行ってもらった is fine.

**EDIT:** Let me summarize this grammar point in my own words. The "Notes"
under ㊦に(2) is saying the following. Please keep in mind that everything
written below is only about に in the sense of "for (the sake of) ～".

  * 彼に浴衣をあげる means "I give a yukata to him". Easy.
  * **However** , 彼に浴衣を着る means nothing (because 着る does not normally take に).
  * **However** , 彼に浴衣を着てあげる means "I wear a yukata _for him_ " even though 着る does not normally take に. This is because 着る is used with あげる, and 着る is a transitive verb that does not take a human direct object.
  * **However** , 彼に死んであげる means nothing, even though there is あげる and 死ぬ is a verb that does not take a direct object whatsoever. This is because 死ぬ is intransitive! Only in this specific situation, "An intransitive verb can never take に" (in the sense of `for the sake of ～`) is true.
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answer
できる can also mean that "something is possible".  
In this case the "something" is the subject of the sentence.  
Example:  
この仕事は私には出来ません。  
This job is too difficult for me.

[https://dictionary.goo.ne.jp/word/en/出来る/#je-51361](https://dictionary.goo.ne.jp/word/en/%E5%87%BA%E6%9D%A5%E3%82%8B/#je-51361)  
[https://dictionary.goo.ne.jp/jn/151118/meaning/m0u/出来る/](https://dictionary.goo.ne.jp/jn/151118/meaning/m0u/%E5%87%BA%E6%9D%A5%E3%82%8B/)
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