Interesting. The internet is an amazing research tool. In a small amount of time one can do an exhaustive search on things written. It does not say in scripture what you wrote (It is written...but I say unto you...). That comes from an earthly author who was incorrect, which one can find "on the net", and verify the writer's error with any of many bible search websites. The author made an incorrect assertion that "It has been said..." (big difference) can be translated as "it is written". It can't.
The phrase "but I say unto you" can be found in many places in the beatitudes already mentioned above. No contradictions, rather, our Lord was explaining scripture to Israel for our learning.
He did that for Israel first, who rejected Him. He did that for us later, and today, through His chosen apostle St. Paul. He opens up scripture, not contradicts it. For us (Luke 24:30-32) through the breaking of bread.
But, it's good to search seeming contradictions as there is learning there. Thanks!