This is something that I have looked into before, and found a fairly definitive explanation.
Fennel, like many other plants in the parsley/carrot family, originated in summer-dry climates. In order to prevent the seeds from sprouting when there is not enough water for the plants to get well-established before the soil dries, their seeds are coated with natural germination inhibitors. Ever wonder why carrots and parsnips take so long to germinate? It's because the inhibitors must be washed off or biodegraded before the seed can sprout. If you soak and rinse them, they sprout much faster. In germination testing, seed companies routinely soak these seeds before trying to sprout them. In nature, the equivalent of soaking and rinsing is heavy rainfall or seasonal flooding.
Planting a few fennel seeds has little or no effect on neighboring plants. Nor does the presence of the plant itself poison other plants nearby (unlike black walnuts or wormwood, which both secrete poisons from their roots and foliage.) However, unlike carrots and parsnips, fennel is often grown to full maturity and allowed to set seed, which it does prolifically. It also can be perennial in mild climates, and turn into large plants that produce thousands of seeds year after year in the same location. A shower of fennel seeds can leach enough inhibitors into the soil to produce an effect on the germination of crops planted nearby.
You can remove the flower stalks as they start to form (and use them while soft and immature as a vegetable, as is done in Italy) or you can clip the seedheads before the seeds start to fall. Or you can grow fennel among other perennials, since existing plants are unlikely to be affected. I don't know about transplanting crop seedlings into soil where lots of fennel seed has fallen. I doubt that it would do more than slow them slightly; that's a topic for experiment. But as long as you realize that the culprit is a chemical that's found on the surface of the seeds, that the seeds need to be in the soil in fairly large quantities to have an effect, and that the poison is water-soluble, you have the tools to cope with it.
Interestingly, grasses (and other monocots like onions and lilies) tend to be immune to the inhibiting effect of this type of compound. So in climates like mine where fennel is an invasive weed along the roadside, you will see grasses around it, but not most wildflowers, which like many other broadleaf plants, are more sensitive to germination-inhibiting compounds. (Grasses and onions are even immune to juglone, and can grow directly under black walnut trees.)
