With regards to PhD theses, what level of knowledge should one assume the reader to have? And, if needed, where should basic information be placed?
Generally, the target audience of your doctoral dissertation is your doctoral dissertation committee. Write to their level.

In disciplines where your dissertation gets turned into a book (or series of articles), then you may consider writing at a lower level or with explanation for people outside of your specific subfield. You can certainly do this if you have the time or luxury to do so, but if you are short on time or funds, then it is perfectly acceptable to do what is noted in paragraph #1.