Living in my PA house for over 30 years, I've constantly battled getting "nuisance" water in the basement, and I have a sump pump and perimeter drain. The water just percolates up through the floor in certain spots, where the builder didn't grade the floor correctly.
It typically happens when we get a deluge rain after a dry spell, and the dry clay soil can't absorb the water quick enough, until the clay eventually gets saturated and absorbs the water better.
What has improved the situation recently was I reroof'd the house but at the same time upgraded to larger 6k gutters and added additional downspouts. I had noticed that before the upgrade, in heavy rains a lot of water was going over the top of the gutters, as they filled too quickly before they emptied via the downspouts.
I'm now kicking myself that I didn't do this years ago. It's something for the OP to investigate in a heavy rain whether the gutters are overwhelmed.
With basements, the best approach is to find a solution that keeps the water outside (via grading, drains, etc.). It's always better to attack the problem from the outside, instead of the inside (sump pumps, inside waterproofing, etc) since there's a lot of hydrostatic pressure on the foundation walls if water is penetrating them.