I guess that you are familiar with the rule that you don't have to repeat the same word twice in a sentence.
Before last week she hadn't attended class or/nor played football.
This doesn't always work. In general with helping verbs like "have" or "do" you repeat if the two phrases are separated by a comma:
Before last week she hadn't attended class, nor had she played football.
We can use the conjunction nor here to negate the second phrase. You don't have to, but the sentence is a little clunky:
Before last week she hadn't attended class, and she hadn't played football.
There may be reasons why you want to repeat these, for emphasis:
Honey, have you seen our son? He hasn't cleaned his room, he hasn't washed the dishes, and he hasn't done his homework.
If you want to use "hadn't" to mean only the first action, you definitely should separate the two with a comma, and use the appropriate conjunction. This helps make it clear the two are separate actions:
Before last week she hadn't attended class, but she did play football.
If you don't include a conjunction like "but" that changes the direction of the sentence, ordinarily you would assume "hadn't" (or similar helping verb) applies to all the parts of the sentence. Your last example is therefore confusing because it doesn't follow this convention.
The easiest way to interpret it is if you already know something about this news story. There are also some grammar and contextual clues if you read "hadn't" into the other parts of the sentence:
... [Veselntiskaya hadn't] insisted he never told his father about the offer of the Russian government's help.
"Hadn't insisted he never" would be a grammatical but unlikely double negative, plus we are talking about Donald Trump Sr., not Veselentiskaya's father. Anyway, here's how I would have written it to avoid confusion:
Trump Jr. claimed Veselntiskaya hadn't provided anything of substance. Additionally, Trump Jr. insisted he released the e-mail chain himself, and never told his father about the offer of the Russian government's help.
This makes it clear who is doing what.
Side note: What most of the world calls "football", Americans call "soccer". American football is a very different (and awesome) game, but one that women don't normally play.