It's just as easy (if not easier) to make a mistake with a recursive call such that it never terminates. Why did your team suggest it as an alternative and why was it accepted? TBH the whole story seems very hard to believe.
I commend your skepticism, of course, but I don't think that's so hard to believe. I'm sure we all have stories of non-technical managers making stupid decisions based on complete misunderstanding of computers and programming languages and principles, after a quick explanation by a technical person.
I mean, imagine trying to explain recursion to someone who doesn't even really get for-loops.
I can see it.