I read a sentence
彼女はわかっていた。あるいは、わかっていると思っていた。
It was translated as "She knew, or she thought she knew/knows."
Prior to seeing this translation, in my head, I interpreted it as "I knew her, or so I thought."
Is my interpretation valid or not? And if not, why?
Your interpretation is incorrect.
The は in 彼女は clearly indicates that she is the one doing the knowing. Your interpretation would be written as
彼女**を**わかっていた。あるいは、わかっていると思っていた
However, I would translate it a bit differently. I would translate わかる as "understanding" as opposed to "knowing" which would be 知る(しる).
So my translation would be She had understood. Or she thought she had understood. The difference might be negligeable depending on the context, but it feels worth pointing out in this case since there would be a big difference between "I knew her" and "I understood her".
Caution 1: Actually, more senetnces like "Someone understood her, or someone thought that someone understood her" can be meant, but I don't refer to it because nothing would never end.
Caution 2: Probably, "understood" there doesn't mean what "understood" mean in usual English. I just translated "分かっていた" into "understood".
彼女は分かっていた。あるいは、分かっていると思っていた。 can mean these things.
She understood something, or she thought that she understood something.
She understood something, or I thought that she understood something.
I understood her, or I thought I understood her.
The first pattern of sentence structure is used like タカシは浮気をしていないかもしれない。でも、ミワはタカシが浮気をしたことを分かっていた、あるいは分かっていると（ミワは）思っていた。だからミワはタカシに別れ話をしたんだ。
The second is like ミワはタカシに浮気を指摘しなかった。でも、ミワはタカシが浮気をしたことを分かっていた、あるいは分かっていると（僕は）思っていた。だから僕はタカシに彼女を大切にしろと叱ったんだ。
The third is like タカシの3人の浮気相手マコ、ユリ、カナのうちユリとカナが今どこにいるかをミワは知らなかった。でも、マコは分かっていた。あるいは分かっていると思っていた。だからミワはマコの職場に向かったんだ。
Depending on the situation, the three can be meant. But you know the first one is most impressive and beautiful when you read it in a novel or movie's catchphrase even in English, right?
So others have little advantage of using the sentence regardless of its difficulty to tell people the right meaning, and different easy sentences may take place of it.
