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Yes it's native. All Sisyrinchium found in the US are native.
It's probably either Sisyrinchium rosulatum or Sisyrinchium atlanticum.

Hmm...there seems to be a lot of confusion about this genus. The Florida Atlas of Vascular Plants says that Sisyrinchium rosulatum is non-native. http://florida.plantatlas.usf.... Other sites say it's native, some say it was introduced from South America. The Plant Atlas also considers Sisyrinchium atlanticum a synonym for Sisyrinchium angustifolium. I have that species in my front yard but wondered why the ones in the back had pink flowers which I had never seen before. Thanks for your help!

ITIS shows Sisyrinchium atlanticum as an accepted name. For nativity and distribution info, I usually use BONAP. Here is the maps for Sisyrinchium.
http://bonap.net/NAPA/TaxonMap... They also show S. atlanticum and S. angustifolium as two separate species.

Flower color tends to vary a lot among individual Sisyrinchium plants, even within a single species. I've seen pastures covered with Sisyrinchium campestre plants blooming in an amazing array of colors including white, light blue, dark blue, violet, and pink.