Buick had ridden the Mark Johnston-trained Permian to finish last in the Grade One Secretariat Stakes when the colt fractured a foreleg and unseated the rider shortly after crossing the line.
Permian had to be put down due to his injury while Johnston's son and assistant, Charlie, reported Buick had been taken to Northwest Community Hospital "complaining of back pain".
Buick's father Walter issued an upbeat bulletin on Sunday, though, and is hopeful the rider could soon be heading back to Britain following a second check.
He said: "William is going to have a second scan and hopefully they can get him on a flight home later today.
"It could have been an awful lot worse. I've spoken to him today and he is in good spirits."