No, we don't have Kio's records. We have a lot of records from other people, but not Kio. I re-checked Casey's records recently and confirmed no calls to/from Kio during any relevant time period, but yes, technically if Casey used another phone she could have called Kio on July 9. If she did, though, it seems pretty apparent that Caylee was not talking in the background, as the car was at the tow yard June 30-July 15 with decomp smell and Caylee's decomposed hair in the trunk.
Have a look at the link I just provided, on August 12th 2008 Kiomarie states that she now realizes that the Casey she got a call from (with child in the background) was Casey Williams, asking for money.