Definitely not true. I worked at a grocery store a long time ago. A power outage that lasted three days caused the egg case to smell horrendous. Hundreds of eggs were spoiling within a few days.
Actually it definitely is true. In most countries in the world except the US eggs are not refrigerated at all.
You probably had some broken eggs, or an egg had broken in the past and was never fully cleaned. The unbroken eggs were fine, but the smell from the broken ones was getting into them.
Egg's are washed which results in the membrane on the outside being removed. This allows easier access for bacteria if not refrigerated.