Whilst theres been no solid confirmation on the shows behalf, its been implied and speculated that Supergirl takes place in the same realm as the greater DC Cinematic Universe. With that said, it was a little hard to swallow when Kara tells Alex that Superman doesnt kill people. If this series does take place in the same universe as the DCCU and Man of Steel then clearly Kara has a skewed perspective when it comes to her cousin. After all, it was in Man of Steel that we saw the Big Blue Boy Scout snap the neck of General Zod.