Can the off-regional pokémon hatch from eggs?

Some people claim you can get the pokémon that are not in your region from eggs. Is this only a rumour or actually true? I've seen off-regional pokémon in gyms nearby but I can't rule out that the owner had been abroad or maybe even used location spoofing.

Solution 1:

Silph Road reported in their Study #6, published 2016/12/29, that regional Pokemon are no longer available from eggs. The study examined over 1600 eggs. It also includes a quote from John Hanke, Niantic's founder and CEO, saying that even when they were available, the eggs could be found only within their regions.

Solution 2:

It is almost certainly impossible.

While many people claim to know someone whose friend hatched one, this can always be explained by someone lying, spoofing, account trading, or actually travelling to that location.

The Silph Road ran tests of over 40,000 eggs. Not a single one hatched into an extraregional pokemon.

There is, meanwhile, no documented, proven case of a pokemon hatching from an egg this way. Even if Silph Road hadn't done an extensive study, the burden of proof would still be on proving they can hatch, not that they can't.

Solution 3:

Yes you can get region locked pokemon from eggs and I believe all of the region locked pokemon are from 5km eggs specifically.

Sources for egg here, example here