I have no idea what the impact of trees on subsurface water flow is in urban areas with lots of pavement, but I'm willing to take it on faith that it's positive, based on my experience in rural Ohio. (In more exposed areas, they also have the salutary effect of breaking the wind--at least until the wind, in turn, breaks the trees, which is why you want them a short distance away from your home, but not too far.)
Granted, trees are no substitute for a good stormwater system, but the two are not mutually exclusive.
Back on the main point of the Rethinking Streets video, though: The point that they make about the changing demographics affecting the residential real estate market (and getting lost in the story about the mortgage lending market meltdown in 2008) is well taken. The woman's point about how expectations of future resale value affect current value is sound economics and often overlooked as well. Likewise, the point about how many suburban building codes affirmatively prohibit mixed-use and high-density development has been a longstanding concern--if developers think that single-use residential developments won't sell well and you won't even *let* them build mixed-use developments, or you make the "default" single, segregated uses and make people jump through massive amounts of hoops to get permission for dense, mixed-use development, then the developers will simply go elsewhere. Mixed-use developments, high density developments, and flush frontage in particular should be simply designated as OK to build.
I also note that the speakers had real praise for Easton there, giving it credit as a mixed-use development (even though it's obviously autocentric). That attitude isn't often seen in urbanist proselytization videos.