Learn English – A word for when two statements are both true or both false

Jack of all trades is the term that immediately comes to mind. Very common: check. Doesn't connote that the person in question is particularly good at any particular trade: check. In your case, "all" just happens to amount to two, which is not a problem and would be perfectly clear from context.

Edit in response to your comment: Jacks of all trades is fine. And of course the more constraints you keep considering, the less likely it is you will get a result that's less weird, or indeed that you get a result at all.

That being said, since you are aiming for a single-word agent noun, all you need to think of is a verb to derive it from. You have viewer for people who view, listener for people who listen, and so on. Now, since you specifically didn't mention what the other type of activity was, we can't think of a verb that would mean "view + the other activity", but have to go with a very generic verb for "doing more than one thing at once". For which the most common word in my book is multitasking.

So your single-word agent noun would be multitasker.

Two often misunderstood terms come to mind.

You could say that the idiom begs the question:

To beg a question means to assume the conclusion of an argument—a type of circular reasoning. This is an informal fallacy, in which an arguer includes the conclusion to be proven within a premise of the argument, often in an indirect way such that its presence within the premise is hidden or at least not easily apparent.

People often use "begs the question" to mean "raises the question", but its original meaning was including an assumption in a statement about that assumption- such as the fact that geese are easily scared.

You might also call the idiom a factoid:

The term factoid can in common usage mean either a false or spurious statement presented as a fact, as well as (according to Merriam Webster and the Oxford English Dictionary) a true, if brief or trivial item of news or information. The term was coined originally in 1973 as a neologism by American writer Norman Mailer to mean a "piece of information that becomes accepted as a fact even though it’s not actually true, or an invented fact believed to be true because it appears in print." Since its creation in 1973 the term has evolved from its original meaning, in common usage, and has assumed other meanings, particularly being used to describe a brief or trivial item of news or information. So it is a factoid that "factoid" means something that is true.

People often use "factoid" to mean "a small fact", but its original meaning was a false statement that was repeated so often that people thought it was true- such as the fact that geese are easily scared.