i was taught that verbs are either transitive or intransitive.
That is unfortunate, because the claim is misleading as long as Japanese is concerned.
Unlike English, Japanese does not have a strict distinction between transitive and intransitive verbs. Although some people categorize the verbs which can be used with ～を as transitive verbs and the other verbs as intransitive verbs, ～を is just one of the modifiers of a verb in the same way as ～に and ～から, and these modifiers are optional.
- ケーキが冷蔵庫に入っているけど、食べないでね。 There is a cake in the fridge, but do not eat it.
- 昨日は朝まで飲んだ。 I drank overnight yesterday. (From sawa’s answer)
In these sentences, are 食べる and 飲む transitive verbs with ～を modifiers omitted, or intransitive verbs? I cannot see any point distinguishing these two.
So in Japanese, classifying all verbs to either transitive and intransitive does not have much use.
What is useful is the transitive-intransitive correspondence such as 動かす and 動く. Note that even in this case, 動かす can be used without an ～を modifier.
わかる usually takes ～が when specifying what is understood, but ～を is also used in some contexts, as stated in the page which you linked to. One can describe this as “わかる is usually used as an intransitive verb, but can sometimes also be used as a transitive verb,” but I do not think that this explanation makes the situation any easier to understand.