‘Could’ specifies a possibility of an event occurring, as opposed to no possibility.

For example, I could have rice for dinner, however there is no way I could jump to the moon.

When applied to the context of this conversation:

A person born in the 90s could have had their childhood affected by the recession in the 80s. A person born in the 50s could not have had their childhood affected by the recession in the 80s.

Could is only vague in the scope of probability; this is because it’s a confirmation of the possibility, rather than a defined probability.