What's even more ironic is that Watson and Crick did NOT discover the DNA. Actually, a woman did. Not only she hasn't been rewarded economically but even culturally-wise.
She was not left uncredited but is less well known. She didn’t share the Nobel Prize mostly because she had died and rightly or wrongly it’s not awarded posthumously.
Photograph 51 is a good play about Rosalind Franklin BTW.
No, she most certainly did not discover the DNA. The DNA (which was not named like that) had been around since Friedrich Miescher's work in the 19th century.
Your statement is at least[#] as ignorant as saying that J.J. Thompson discovered electricity since he discovered the electron. Of course, the electricity had been discovered long before that.
[#] What I have in mind here is that even the statement that she discovered the molecular structure of the DNA is not strictly speaking accurate.