freediver:
An aquatic emergency? A trained, prepared lifeguard. Perhaps maturity was a factor here but with all things being equal, I'm not sure what the doctor or nurse could have done that the lifeguard could not have done given the equipment on site. Without specifics, it's hard to say. This is certainly a scenario that in-service training would have prepared them for. It is tragic nevertheless.
I'd go with the trained, prepared lifegaurd. While it's true that doctors/nurses do have training, there is a big difference between a patient in the ER and a patient on a pool deck. When I was taking my OFA III course the question arose "If there is a doctor/nurse at the scene would the victim be better off being cared for by them?" the answer, in short form, was "no". A paramedic however would be an entirely different story.
Personally, if I were attending a victim and some dude in swimming trunks came up to me and said "I'm a doctor, let me help" they'd be my first choice when asking for assistance but there's no way I'd let them take over - How do I know that they're not just joe blow with some basic first aid training and a superiority complex?
After that bit of a rant it does sound like the lifeguards were somewhat negligent and were probably freaking out at the time, being the only drowning they'd ever had to deal with but lacking the full story and not having been at the scene it's not possible to cast judgement. As for the comment about the masks leaking and children choaking on the water, it's ridiculous. It sounds like they're sayng that children are more likely to suck water up their nose with a mask on then with their nose exposed to the water.
It is a tragedy yes and my sympathies go out to all involved, life guards included (those guys are probably going to need therapy after having a kid die on their watch) but ultimately I have to question, where was mom and why did she leave her child, obviously not a strong swimmer, unattended?