@SimpleCycle -
The usual rule is that you owe taxes on all income in your resident state. But you typically get a tax credit there for income taxes paid in other states, so you are not double-taxed.
Then you owe taxes only on income earned in that state for non-resident states. Each state sets their own rules regarding when you might owe taxes to that state. Some states, you technically owe taxes in the first minute you work there. Other states have an income limit you have to hit before you owe in that state.
Simplifying matters for the majority, but adding yet another layer of rules - several states have reciprocity agreements in place, which usually means if you live in one / work in one of those states that yours has a reciprocity agreement with, you'd only owe taxes in your resident state.
So maybe the specific set of states you've worked in are either "no income tax" states or have reciprocity in place with your resident state? Or maybe your employer is not doing things quite right?
Either way, for practical purposes, filing based on the documents your employer sent you is probably fine, particularly if you're not making boatloads of money in a bunch of different states - are they really going to go through the effort to chase you down if you owe $200? Probably not. How would they even find this out? Juice is typically not worth the squeeze if your employer is not reporting income to a state, even if they should. Doesn't mean the rules aren't there, but if they are impractical to enforce, do they really matter?
Major league athletes have a problem flying under the radar on this - their salaries are often publicly known or can be estimated pretty easily. Then you play a game in a stadium that holds 20,000 to 80,000 and is advertised widely, so it is easy for the taxing authorities to know if they owe some income tax to a given state or locality, and for some it is a substantial amount.
There has been legislation proposed at the federal level that would establish a nation-wide "you don't have to file in a non-resident state unless you work 30 days in that state during the year" rule, but as far as I know, it hasn't been made law yet.