Pyramus and Thisbe or Romeo and Juliet?

After every Greek myth I read, I begin to understand that it is indeed, as all my teachers have taught me since 4th grade, the basis of western civilization. From previous myths, I have seen that many religious stories are based on these myths, and after reading Pyramus and Thisbe, I recognize that literature has also taken a big part from Greek mythology. Pyramus and Thisbe is pretty much the same exact story as the most famous play ever written: Romeo and Juliet. Is it just coincidence, or did Shakespeare know of this myth when he wrote the play? Being the most famous writer of the time, Shakespeare had to be familiar with Greek mythology, and thus, I believe he based Romeo and Juliet on Pyramus and Thisbe. I am not taking anything away from Shakespeare, however, as I have personally read Romeo and Juliet, and believe that it is fantastic. You do have to ask yourself though, do all great things in theater and literature come from the Greeks, or is there imagination somewhere down the line?