I am a little rusty on this since it has been a few years since I looked into this. But the answer to this question is, it depends...
There are two distinct classifications of moving streams in Iowa, meandering v. non-meandering. At any rate, there are two fairly different sets of rules that apply based upon the stream classification.
If a steam is classified as meandering then the river bottom, the shoreline up to the permanent vegetation line and so forth is considered public access. The larger rivers like the Cedar, Iowa, etc, are considered meandering. In this case you can wade the stream, camp or build a duck blind on the sandbars, walk the bank below the highwater mark, etc, and do so without trespassing, regardless of whether the adjacent land is posted or not.
Now then, if the stream is classed as non-meandered , then the adjacent landowners rights apply and you can be considered trespassing if you are not floating. Technically speaking, jumping out of a canoe and touching the bottom is considered trespassing, etc. I know the Upper Iowa River is non-meandered, giving the farmers the right to stretch a fence across the stream to keep cattle in, etc. (This can lead to a bad mix of high water and canoes, but don't ask me how I know this!) It gets a little more complicated if the adjacent land is posted on a non-meandering stream. You should double check this, but I think I remember that you can be charged with criminal trespassing if you walk/wade/etc on posted ground on a non-meandering stream.
So, find out how the stream you are referring too is classed and go from there. But I will guess from what I read in your original post that this person is probably pretty close to true.
Good luck.