It's not that Kansas or Oklahoma has the rule. It's whether the FBI NICS center will accept a state's CCW permit in lieu of their own background check. What I've heard about Oklahoma is that since the state offers a 10 year SDA card (I cannot bring myself to call it a "handgun license") the ATF and/or the FBI won't accept them for background checks.
I hold a 10-year SDA card & would be glad to roll back to a 5-year if that would give us the NICS exemption. We had the exemption until about 2000 and then we didn't. The 10-year SDA didn't come along until after that so something else changed at that time and I've never heard anyone speak with specificity as to what that was beyond a BATFE publication that simply stated OK was no longer on the accepted list.