Sure in retrospect it would have been a good idea to have staked these trees. But then who knew we would have what? almost 10" of rain in 3 weeks! Ideas about staking have changed over time as tree planting techniques have been refined. A tremendous amount of research has been done in recent years regarding selecting, siting, planting, and maintaining urban trees. Cornell University's Institute of Urban Horticulture and Bartlett Trees are at the forefront of this work. Both offer on their sites, useful and informative downloadable publications. Both also observe that staking ought only to be done in special situations, i.e. when the tree may come down if you don't stake it! Ha Ha!
It isn't always easy to tell when that will be. I don't know when those trees were planted but if they were planted in the fall after most of their leaves were gone, it was reasonable to expect that they would have rooted out enough to support themselves before the leaf canopy filled out sufficiently to catch enough wind to blow the tree over. Fall is the best season, by far, to plant trees so lets be generous and assume they did the right thing, the trees went in in the fall, and its just bad luck that the soil turned to soup.
Back to whether to stake or not. So, if you plant in the fall and the tree is deciduous you normally don't stake. Exceptions would be a tree with a leafy top out of proportion to its root ball. If the ball isn't heavy enough to hold the tree, stake it. If you plant an evergreen in the fall, stake it, cause the winter winds will have their way with it. Planting in the spring is the trickiest. If you plant before the leaves are out and the top is in good proportion to the rootball, you shouldn't have to stake; the new roots should grip enough to support the tree. If you do stake, be sure to remove the support after one year. The proper development of both top and bottom depend on movement of the top in the wind. Oh yeah, about summer and winter. Winter is easy, its the same as spring staking-wise. Summer....try not to plant in summer, but if you do it is probably a good idea to stake as a defense against the winds of thunderstorms.