Can a clogged gutter cause a leak?

Hi,
We have had a tremendous leak in our house. Our ceiling was leaking through the seams for 4 hours after the rain had ended filling up two entire garbage cans (50 gallons each). Our landlord (who has proven to be quite cheap) climbed on the roof and discovered a ball that was clogging the path to the gutter, I guess. He says that the problem is probably solved.
Can that be so? Or would it take a combination of a clogged gutter AND a whole in the roof to cause such a significant leak?
Many thanks in advance,
Aaron
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We had a leak that never happened again after we cleared the gutters. Yes, it can happen.
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