I'd be curious what you as an instructor, or other instructors on this thread, would do if you had a student who aborted the 4th dive of OW due to an asthma attack underwater. Would you let them dive again or tell them they need to see the doctor again and can come back on the next trip to complete certification? .
Heck, I'm certainly not an instructor, but if I witnessed that during my ow classes/dives that I would tell the instructor that the person should not dive again until they were cleared again. Even I knew that. Unfortunately if the instructor said it would be ok with a day of rest, I probably would believe him--Trust in meeee, just in meee says Kaa.
If I saw that now, for example in another class or a group dive, I would probably not feel comfortable diving with that person, and would encourage them to sit it out. If they didn't, I would. I don't want to see anyone die diving, and I would be more of a help topside just in case.
waiting to see what instructors say....