I did some searching, today, and found some kind of basis for what the article I read said.
Apparently, "… [potassium nitrate] has long been used to stimulate germination of weeds …" according to this article (with other similarly interesting statements), which is about a study testing ammonium nitrate on lambsquarter and velvetleaf, to see how it influenced seed dormancy and germination. It didn't affect the velvetleaf, but it did seem to affect the lambsquarter. I'm unclear as to whether it affected the amaranth.
Here's another article that talks about different chemicals that were experimentally used to see if they induced germination (they said they did), and one of them was potassium nitrate.
So, it seems it's more than one person who thinks its true, and that there is some kind of basis in study for it (although they still don't overtly say why they think it's true). The first also says that weed seeds have higher ammonium nitrate levels than crop seeds, which trait they suspected wad related to dormancy. I wonder if by weed seeds, they mean overwintered seeds, or any seeds that haven't been bred to germinate easily/predictably in controlled conditions, or whatever kind of seeds.
Okay, I found another article about an experiment with various substances, including a few nitrates, and this is the reason they quote why nitrates are supposed to induce germination in a certain kind of seed:
"It is found that nitrates are capable of breaking the dormancy ofAvena [sic] sterilis spp.macrocarpa Mo. seeds, which according to various authors, is due to an increase of the respiratory activity of the seeds"
I'm not sure how nitrates increase respiratory activity of seeds, though.