The guy who was on a kayak and decided to bring his 10lb dinner bell dog with him to a lake is just dumb. That story is the story everyone uses about what not to do when in a kayak, it is like living on a lake, and leaving your dog chained outside and then wondering how it ran away?
If Kayaks were Dangerous because of Gators, They would not rent them at Every State Park, Lake Toho, Harris, and have Kayak trips on the Hillsbourough River here in Tampa where it is loaded with Gators. If people were getting attacked they would not be renting them since insurance would put them out of business, plus it was common for Guides and older Angler's to Wade Fish the Shallow Florida Lakes on the Kissimmee Chain like Toho, and I read Larry Larsen's book on Florida Bass Fishing and he pretty much spent 30 years wading in salt and Freshwater with Sharks and Gators, people still fish out of a Float tube on Lakes, water Ski, I could go on and on...You are more likely to get killed driving to the lake or drowning due to your boat or Kayak sinking and not having a life vest, crashing your bass boat while doing 70mph after naming it the "Intimidator" in 2.6 feet of water in an airboat trail 5 feet wide, getting lost in the fog without a GPS or Navigation system etc. Last year 2 fisherman drown here in Lake Tarpon while Crappie fishing in their Jon boat while anchored in 14' of water in an area where the wind picks up quickly without warning and can cause some pretty big waves that just so happened to be large enough to come over the bow and sink the boat. They 2 guys were only maybe 1/2 mile out on a lake surrounded with houses all with boats tied up to docks, restaurants, parks etc, but they did not have a flare gun, whistle, ability to swim, nothing in the boat as a floatation device.
I understand your logic and it is quite common for people to avoid certain activities for safety reasons and I do not fault them for that since we all have fears of being attacked by a Deer while filming nature, or gators, or whatever....I have made many mistakes on the water in my life and I have learned from them and I simply respect the outdoors, prepare for the worst if it happens, but if I were to be attacked by an alligator while fishing and not breaking any golden rules of safety then so be it...I am much more likely to die by lighting strike to be honest since I often push that one a bit too far when the fishing is good (I use my fiberglass rod to be safe)...
People swim with Great White Sharks, I like to Bass Fish at night, and I know how to swim, navigate, and I do not float tube personally although when I lived in NY and was in college I did it all the time, and people would always tell me I am crazy because of "Snapping Turtles"...fear of the unknown is normal, but I still feel like the fins on my feet make me look like a giant turtle in a float tube, so I do not do it, but when I see someone else doing it I just figure they know the lake and habits of predators in the lake.....Sorry for the ramble, I get frustrated when friends from work will ask me to take them fishing after work and when I tell them that we are taking a hike into the woods and fishing till midnight, they skip out because I am crazy and that is dangerous, so they go to happy hour instead, have a few drinks, and drive home nice and relaxed thinking how I take stupid risks just to catch fish....