Does the strength of the barrier between egg yolk and white indicate freshness?

Often you can plop eggs out of the shell on a pan nicely, so that the yolk remains whole and doesn’t leak out to mix with the white. But other times, the barrier between the yolk and the white is so fragile, that there is some disintegration and some of the yolk leaks out when you try to get it on the pan. Also it becomes difficult to separate the yolk and white.

Does this indicate the eggs are less fresh?

I have the eggs sitting in ambient temperature of 30°C (around 86°F for those using exotic units), this is the room temperature. I have a suspicion that this (egg yolk leaking) happens more for eggs which have been sitting more days since collection, but I am not sure yet if there is a correlation.