In the US, is it relatively common to see houses built near riverbeds? I mean, there's St Louis, for example, but I dunno on a residential scale.
Unfortunately, yes. Typically farmland, but also whole towns are built in the flood plains. And people hope the Army Corps keeps the damns working.
Annual flooding here in the Midwest is a BIG deal. Last year they blew a dyke in downstate Illinois to save one town and washed away everything on the other side of the dyke, which was mostly farmland.
Construction on pilings is a common practice, though I don't know how common for a single family home but I would guess uncommon. What it basically means is that the soil won't support what you're doing.
Get a local professional. Someone there has dealt with this. How to get a good reference for who to deal with is an important question.