Other groups also want schools and teams to have heart defibrillators at games, and have coaches and parents learn CPR.
The European Society of Cardiology and International Olympic Committee endorsed standardized screenings that have been credited with lowering the sudden cardiac death rate in Italy.
But previous U.S. studies suggest no added benefit from such screening methods, and U.S. medical groups don't recommend them. Although ECG screening may not have made a difference for Hammerdorfer, since he'd been previously diagnosed with a congenital heart problem, it is not known whether such testing could potentially benefit athletes like Leonard, who had no clues.
One argument against standardized electrocardiograph screenings for all athletes is that they cost too much. Some believe the money could be better spent putting automatic external defibrillators at every sporting event.
Dr. Douglas Zipes, editor of Heart Rhythm, told ABC News that to cover the $1,200 cost of a defibrillator, "you could get 120 fathers to kick in 12 bucks each."
There's also the danger of false positives -- suggesting that athletes are at risk when they are not -- with such blanket screeing. And ECGs are unlikely to detect certain types of heart problems in some, said Dr. Brian Olshansky, a professor of medicine at the University of Iowa Hospitals.
For every 200,000 people screened, it is estimated that only one would yield a true positive for a heart abnormality. "The overall value of an EKG screening program remains highly problematic," said Olshansky.
Ackerman acknowledged that for some families who have lost a loved one to sudden cardiac death, a false positive could be seen "an acceptable nuisance." But he said the rate would be too high for it to become an acceptable way of determining who's at risk.
"Overdiagnosis is not trivial, and it can be just as tragic as missing it in somebody," Ackerman said, adding that it could lead to the sidelining of too many athletes.
While blanket screening may not be an adequate method to detect congenital heart problems that contribute to sudden death, Ackerman said there are steps families would take right away.
"Know your personal story, know your family history and advocate for a community rapid AED," an automated external defibrillator, said Ackerman.
ABC News' Clayton Sandell and Kevin Dolak contributed to this report.