Some background from a portion of the book Soviet Space Dogs suggests that this claim was most likely propaganda written as a response to the protests described in the answer above, but offers no proof for or against the claim.
The international press accused the Soviet totalitarian regime of
inhumanity, and suggested that General Secretary Khrushchev should
have been sent into orbit instead. In response, the Soviet press wrote
about the hypocrisy of capitalist morality, the exploitation of entire
nations in the colonies, and racism.
In his book Trecioji dolerio puse (The Third Side of a Dollar, 1964),
Albertas Laurinciukas, an American correspondent for the newspaper
Selskaia Zhizn (Country Life), mentions the following anecdote. In the
aftermath of Laika’s launch the United Nations received a letter from
a group of women in the state of Mississippi, who condemned the
inhumane treatment of dogs in the USSR, suggesting that if it were
absolutely necessary to send a living being into space, why not send a
group of Negro children, (of whom there were plenty in their town),
rather than a poor dog.
It’s hard to imagine that such a letter ever really existed , but the
USSR’s official anti-racism policy was a strong weapon in the Cold War
against the USA. Regardless of these arguments, Soviet ideology was
faced with a serious dilemma. Since denying Laika’s death was
impossible, their only viable option was to immortalise her.