I honestly don't know the answer to your question, and it will take some time to find an answer.
The reason for this is that these sites are not covered by "gambling" laws. I have made it a point to keep a good and generally up to date list of the various state gambling laws, and this forum is here to help keep all PPA members informed as to how those laws affect their ability to play poker.
With these sites, you are not really playing poker as we traditionally know it. Although I also do not know the details on all these sites, SpadeClub and ClubWPT both work from the premise that what they are offering is a "sweepstakes" style competition, not a card game (even though you get to play cards it is not run like Pokerstars or Las Vegas Casinos). If you look at the fine print at these sites, you will find that NO money is ever directly wagered on a game. In fact, they really dont have "cash' games at all (except ones that only use "play" money), just plenty of tournaments where "prizes" can be won. All also allow anyone to play in those tournaments for free (again in the fine print: you must send a handwritten 3X5 card etc...). Of course, if you buy their membership you are relieved of the burden of having to send the cards, but you dont HAVE to buy the membership to play.
Thus this business model is not "gambling" as their is no "consideration" REQUIRED to play the tournament.
Some states, however, have specific statutes covering these "sweepstakes" style operations, and apparently Ohio is one of those. It either bans them directly or (more likely given the difference between the sites) requires certain conditions or licenses that possibly ClubWPT has met but SpadeClub has not. Of course, the difference could also be a difference of legal opinion.
It would take me some time to get access to Ohio sweepstakes law. It might be quicker if you do this yourself at the OHIO state website. If you wont or cant, let me know and I will check it out when I have some spare time.
Thanks for the question,
Skallagrim
PS, I am not familiar with Poker School Online at all; if their operation is different from the other two I mentioned, please post the details and I will respond as best I can.