The link describes how the hybrid(s) is made, through non-natural circumstances, and not just by a human simply dabbing pollen where it doesn't usually go.
One of the basic tenets (but often inaccurate) of a species is "breeding within its own kind".
But you are right to be suspicious. In some genera (Aquilegia, for instance) species within the genus cross very easily. On the other hand, there are genera where the species NEVER cross (Impatiens, for instance). As you might guess, most plants fall somewhere in between.
Within the Allium genus, there are hundreds of species, and whether a hybrid between any of them is even possible, depends on how closely they are related. Desert alliums are distantly related to Allium cernuum, that is native to New York. They would never cross naturally. But Allum cernuum and A. stellatum are closely related, and grown in proximity, there is a strong chance that they could hybridize.
Our Perennial Plant of the Year, Allium 'Millenium' is a chance hybrid, perhaps even between mulitple allium species.
Both onions and garlics have been bred by humans out of the wild for millenia, which would distance their relationship even more. Their morphology suggests they are far apart:
-- onions have round, hollow leaves. garlic has flat, solid leaves.
-- bulbs are completely different, too.
Garlic rarely produces seed anyway. What you see are actually baby bulbs. I don't think they would ever cross.
I don't think garlic and onion would ever cross.
