I witnessed a Parent, whilst filling out this form for their young child (12?), filling out all the no's. The child said "But Daddy what about my Asthma?" to which the Parent made very strong body language suggestions that the child keep that quiet. Fortunately the Dive Instructor saw this too and stated very clearly to the Parent that no matter what he now wrote on the form, he (the instructor) wanted a clearance certificate from a Doctor before he or anyone at that Centre would take the child into the water.
So, with specific regard to the statement that lying on the form can kill you, I would have to agree. In this instance, by lying, you would have removed another safety net which, had you sought professional guidance, may other wise not have allowed you to enter the water.
Best Regards
Richard