Yes, you have a misconception of recruiting at every level of college baseball. DIII can be a verbal commitment only and it operates just like a verbal to DI, DII, NAIA or JC. Many of those players with a verbal get recruited right up to the NLI signing or day they attend the first class, for DIII.
After our son signed his paperwork and made his deposit at Trinity U, he was extensively recruited during the Summer after his senior year by 3 DI's and the local JC coach.
As a DI assistant, his school received a verbal from a player they found and really liked. That player continued to be recruited, switched his verbal twice, finally signed an NLI, got drafted and signed with MLB.