Well, I’d hesitate to call it hogwash because I don’t want to offend Kaloseans.
But yes, it’s very unlikely that phantump are the lost souls of dead children. The same can be said for all ghost-types, actually.
Now, on the other hand, the thing about exeggutor dropping a “head” and having it grow into another exeggcute is actually true. Sort of. Those really are eggs, but they’re virtually indistinguishable from an exeggutor head. And yes, the exeggutor’s reproductive system is located in the head region, not lower down.
For those of you who could have gone your whole lives not knowing the alien mechanics of exeggutor reproduction … you’re welcome.