I’m thinking と wearing its “quotation marker” hat. What you’re saying is ‘I believe “you stole the candy” ‘. 私は君がキャンディーを盗んだと思います。

Another option is the nominaliser こと – basically turns what comes before into a noun-phrase. 君がキャンディーを盗んだことは思います。

Grammar dictionary says “と is used to mark the content of such actions as 思う, 考える, 書く, 聞く and 説明する”, which is basically exactly what you were theorising, but I don’t know if that’s an exhaustive list. Anyway, an example sentence given here is これは十六世紀に建てられたと書いてあります (‘It is written that this was built in the sixteenth century’)

こと turns the sentence preceeding it into a noun phrase, which means you can do whatever to it that you would a regular noun. What makes things a hair more complex is that の can also function as a nominaliser, with the same meaning and effect, but it carries slightly different subtleties. Grammar dictionary says “In contrast to another nominaliser の, こと tends to indicate something the speaker does not feel close to. Thus, in the example sentence 小説を書くことは難しい (‘Writing a novel is hard’) the nominaliser こと indicates that the speaker of the sentence is not particularly involved in writing a novel; in other words, he is stating the sentence in general or objective terms. The nominaliser の, however, indicates something which the speaker can directly perceive or empathise with. Therefore if こと in the example sentence is replaced with の, the nominaliser now indicates that the speaker of the sentence is somehow personally involved with writing a novel; in short, he is empathetic with the act of writing a novel.”

It then gives a few examples where it doesn’t make sense to use one or the other of の or こと, then finishes up with a note about how the K-sound of the word itself makes こと sound more impersonal than the N-sound of の.

Hope that helps. =)