Depends on the dog's size, how many seeds are involved, and most important of all, whether the seeds get chewed open, or swallowed whole. Apple seeds DO have cyanide, no dispute. But the quantity is so small as to be NEARLY a non-issue unless you're talking about something like a teacup chihuahua snarfing down massive quantities of them - and actually crushing them or chewing them open in the process... that part is crucial. Apple seeds are built tough because they're INTENDED to be eaten by critters, then pooped out scattered far and wide from the parent plant, complete with a nice pile of fertilizer to give 'em a boost come sprouting time. In canines, due to their tooth structure, and the typical "rip and gulp" method of feeding, this usually means they pass through the gut untouched beyond some minor surface etching from stomach acid/other digestive juices. (surface etching that, I might add, actually enhances the seed's ability to sprout when the time comes)
Overall, apple seeds in dogs are more of a "mechanical" issue than a toxicity problem - enough of them ingested at once can "pile up" and cause a physical blockage in the gut, similar to the condition a horse person would call "sand colic". Even then, the toughness of the seed, combined with the tiny amount of cyanide in each one, means that the actual, realistic risk of cyanide poisoning is close to nil. (Which isn't to say that a dog can't die from a gut blockage if they hog down a bunch of apples, but a gut blockage is totally different from cyanide poisoning)
Peach, apricot, plum, and the other large-ish "pit-fruits", (Cherries are on the list, too, but like apple seeds, they're usually small enough that for a canine, they almost always get swallowed whole, and pass through essentially untouched) on the other hand, are a relatively serious threat due to both larger physical size, and larger concentration of cyanide per seed. They're big enough to be used as a "chew toy" for some breeds, and can possibly be cracked or otherwise opened before being swallowed, whereas apple seeds and cherry pits almost always get swallowed intact and just pop out the other end in nearly the same condition they went in.
Basically, the fretting about apples being bad for dogs is a knee-jerk overreaction to the idea (true, as far as it goes, but when you look closer at the details, you find it's actually nothing to be particularly concerned about) that their seeds contain cyanide.