I don't doubt what you say. It just makes no sense (and no, I'm not going to spend any time checking). The franchises that pay these players are located where they are located. And pay taxes to that state. Perhaps it has to do with what you are calling "services income"? I can't say that it's what I am going to look up...but I have worked out of state in my career and didn't pay taxes to another state. 
Well, technically, you most likely didn't pay taxes to other states because you didn't fully comply with all of your state tax obligations, but were either too difficult for the state tax authorities to identify, or else did not spend enough time working in any one particular state to make it worth the while for the state tax department to chase you down and assess you for tax.
I'm not saying that to be nasty, btw; plenty of people do not know all of the ins and outs of the tax laws that apply to them every day. For example, did you know that in almost every state, if you buy something from out of state and bring it into your state of residence for use there, you are required to self-report and pay use tax on the fair market value of that property. Other than with respect to large items, like cars, for which the tax is generally assessed and paid when the vehicle is registered, most people aren't aware of this fact and rarely self-report.
But that doesn't change the basic fact that income from the performance of services is sourced to the place where the services are performed, and both the team that plays the game, as well as each individual player who plays in the game, is typically subject to state income tax in the state where they play.
It gets even more fun for people who are partners in partnerships that have activities in multiple states, for example, a national law firm. A partner in, for example, Shearman and Sterling, for example, will often have income derived from 10 or 15 states, and will have to either be reflected on a nonresident partner return filed by the partnership, or else separately file his/her own personal income tax return in each of those states.