Of course; that's why you made your original complaint, which you wouldn't have made in any other case.
So now that you are in a position to listen to the speech while also reading the text, you may well find, as I have, that listening to the speech while reading the text is remarkably useful in training your ear, so that future rapid sentences, not to mention general Esperanto speakers, are more likely to be understandable to you. I presume that's what you're working towards.
I have (very minor) difficulty with the particular voice used in the course. I do not have difficulty with other audio resources I have been using to learn listening skills in Esperanto, hence my complaint about the voice above. The lack of context for sentences here does not help.
This is a positive statement in Esperanto: "She likes [No type of] milk."
The translation suggests a negative statement in English: "She does not like any kind of milk." This has the same effective meaning, but a different semantic meaning.
The statement, "She dislikes all kinds of milk" (Ŝi malŝatas ĉian lakton), is stronger; but that's for the Esperanto style guide.
Ĉian lakton is all kinds of milk, so "She doesn't like all kinds of milk", which is slightly different from liking no kinds of milk. (She might like skim but not 2% or homogenized)
If you go for the double negative, I would say Ŝi ne ŝatas ian lakton, so "She doesn't like any kind of milk"
No, it doesn't. "She does not like any type of milk" means that no type of milk that she likes exists. That's what "any" means in a negative sentence in English. It's not just a denial of the sentence "She likes any type of milk", which would be equivalent to "She likes all types of milk".