It's just strange to see a "no swimming" sign without any other kind of warning unless it's just trespassing. We have them in creeks in our city but they say "stay out of water, RAW SEWAGE!" Pretty clear. Just seems like Disney didn't want to scare people with a more descriptive warning. Plus seeing pictures of that beach it's pretty clear many wouldn't think twice about alligators being in those waters (not everyone is educated about it)
I've heard this a lot and I really think this is what it comes down to. Here are some great shots that sum this up perfect

This is a shot of royal pacific right across from universal. I have to imagine there are gators lurking in there at least there have been. There's literally a sign RIGHT there that says stay out of the water in the photo and yet here is a kid right at the edge in a swim suit, and another who appears to be coming out of the water. The rules aren't strict and I've personally seen this happen on numerous occasions.
there are also pictures of the exact beach with kids and families in the water. I actually dont want to post them because I feel some people would get weirded out given that there are kids closer up in swim suits in what not, but I'll leave this here.
http://forums.wdwmagic.com/threads/bay-lake-seven-seas-lagoon-swimming.15405/
This is a thread asking if it's ok to swim tehre. Multiple people mention it's gross, but safe. Some people say there could be gators, other say there's really no way gators would make it past disney. Plenty of people even locals were unaware, here's a direct quote.
considering that that area of the parks has now been open for 31 years, i seriously doubt that there are (or ever were) any alligators in that water. Just because this is florida does not mean that we have alligators walking la-de-da down the streets. Those bodies of water (one of them man-made) are surrounded by buildings and developments and its not like an alligator is just going to stroll through the polynesian to take a dip in seven seas lagoon. The reason for the ban on swimming is probably due to ameobic infestation of the water. It does happen sometime in central florida. A kid died last year (though not at disney) due to complications of exposure to ameobas (it was in orldando, but at some public lake). Waterskiing is still allowed while swimming is not probably because ameobas will usually reside in the silt (read muck) at the bottom of lakes. If you go swimming, you're walking on that muck and stirring it up, releasing amoebas into the water around you which can then get into your gi tract or other areas you'd rather not have them.
This was prior to the incident, but remember even locals were unaware of the dangers.
edit-
Of course I understand that,but you can't just kill a gator or two, humanely or not. Even if you theoretically kill off the entire area of all gators, they're guaranteed to come back through waterways and swamp land, and come into the perimeters, like where the Resort Hotels/Parks are.
You can kill the gators off, but at the end of the day, it's not going to be effective.
Some urban areas have this issue, it's more than an uphill battle for a company that consist mainly of swamp land and water ways.
It's not about eliminating them altogether, it's about killing them when necessary. Here it was necessary.