Sneakers, Boots, Nike ACG, etc., my .02
Those who could wear sneakers & trail shoes include Thru-hikers that by NH have about 1800 miles behind them. More often than not, people wearing sneakers are not hard-core hikers. Investing in another pair of $60+ specialized footwear - okay they can be worn in winter in CT in town or in Spring & fall - for an activity you may not do again does not make $en$e either.
While I won't doubt Dave, I'd guess that a twisted ankle in a plastic boot would have been much worse unless it was on too loose.
I've been a big boot wearer for years due to multiple broken ankles in other sports, my day hikers had been a Fab/leather Backpacking boot.
This year I did Waumbek in New Balance Cross Trainers & over 30 miles in TN on two hikes & Mansfield in Vasque Alpha's (out of the box new - bought in 1999). However, when on rocky terrain like the Presidentials or this past weekend on 3 or the highest 15 ADK peaks, I wore heavy leather mountaineering boots.
There is something to be said about "feeling" the trail when your feet can handle it or over shorter trips. On longer trips over rocky terrain due to my ankles, I opt for support over "feel" I have not found a boot that after 15+ miles has felt good on the bottom of my feet although the big boots help on ankles. Waumbek, TN, many CT & MA trails at least until you reach the top don't resemble the Presidentials, BSP, Abraham in ME or the ADK High Peaks
When I was at EMS we routinuely would wear the boots around the store so we would know how they felt on our feet which IMO helped recommend boots to customers. While the Nike ACG's seemed designed for narrower feet than mine, I thought they were more of a sneaker than a boot. IMO I had older (late 70's/ 1980's version) leather high top basketball shoes (Puma, Nike pre - Run DMC, Nike before MJ even though about N. Carolina) that provided more support. - not enough apparently in both are cases as my injuries came wearing those shoes, indoor soccer shoes or playing Volleyball.
People's weight, pack weight, strength & conditioning also come into play but that is another rant unto itself.