Blood tests are typically done at jail intake; only typically occur at hospital when injuries are severe enough for admission.
I can't attest to OK jurisdictions, but NV state law (and many others) requires a warrant from a judge: the suspect gets arrested under suspicion of DUI/OWI and booked, while being booked the officer calls the judge on a recorded line and requests the warrant for a blood draw, and then the blood draw is performed towards the end of intake.
If they don't remember the hospital they probably don't remember the jail intake either, which is where the blood draw most likely occurred; if one didn't at intake/at all then a decent lawyer should be able to get it dismissed.