No it's not. You would never put "White and Black Lives Matter" there nor "all people's lives matter".
That's the point! "Black Lives Matter" means something different.
Writing is contextual, if one only looks at the literal then one misses the other half of the meaning. Unfortunately your proposed change has added context that undermine your honourable and well-intentioned message.
As does your original text. Congrats, you made my point for me.