Q: Is the italicised verb form correct in this sentence?
Jane's pale face suggested she could be ill: her parents suggested that she have a medical examination.
A: The sentence is grammatically correct. The subjunctive remains in force even though it is likely the patient will follow the doctor's advice. To actualize the blood test with "has" would be telling an untruth. The subjunctive holds the notion of a suggestion in place. Thus does grammar make its own modest contribution to truthful speaking.
I don't see how this sentence can be grammatical. Please could you offer any comments.