I saw the set list earlier and it did include that song "Alright" (which is reputed to be the "informal anthem of the Black Lives Matter movement).
However, when I searched for the set list just now, I found this note (below), which says that while "Alright" was among the songs performed, the songs were "heavily re-worked" to make them "family friendly" for the White House. I don't know how one would make that song "family friendly" without stripping it bare, but apparently a very different, less offensive version of the song may have been performed for the WH.
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"The highlight of Obama's Presidency"
"Kendrick’s setlist included “Swimming Pools (Drank)”, “Money Trees”, “Bitch Don’t Kill My Vibe”, “Poetic Justice”, “A.D.H.D.”, and “Alright”. Surprisingly, he did not perform “How Much a Dollar Cost”, which President Obama called his favorite song of 2015. Kendrick also heavily reworked the songs to omit any curse words or controversial language — it was a family friendly event at the White House after all!"