It's obvious you two have not been following what the alumni association has been doing. The alumni association no longer collects dues. In order to encourage the alumni to give back to the university, they switched to a gift based model. Prior to 2012, the alumni association had two levels, dues paying members and lifetime members. In 2012, the structure was changed to the...
Lifetime members: Phased out, but those alumni who were already lifetime members are allowed to keep it.
The numbers you are comparing are not really equivalent. The over 500,000 you reference are all graduates of Ohio State (basic members). The 34,000 for Alabama are members giving gifts to their alumni association. I would guess the OSU has more sustaining members than that (couldn't find the number), but they are also able to designate where their money goes. It's possible that Alabama has just as many alumni donating to their university, just not to the alumni association. Also, Alabama does not have a football ticket lottery which would likely increase their membership.