Well so far my only source that there is no source is something that I saw on the internet … I think it was in the Coffee Room in a thread entitled “parshas hamon this Tuesday”…
just joking.. I know you need more of a source to prove something than to disprove it.
But, it’s always good to say it anyhow, so it certainly doesn’t hurt to say it Tuesday of Parshas B’shalach, especially as long as we have no verification that it’s not true. And at least this way, everyone makes sure to say it at least once a year, since every day is too much for most people.