Confirmed by Game Informer, a Sony statement said the following:
One reason this maybe is that while players are technically sharing the game's universe, and could run into one another, No Man's Sky's 18 quintillion possible locations makes the chances of such an encounter statistically improbable.
PS Plus won’t be a requirement to play online, however you will need to be connected to the internet for your discoveries to register with the universal atlas.
One reason this maybe is that while players are technically sharing the game's universe, and could run into one another, No Man's Sky's 18 quintillion possible locations makes the chances of such an encounter statistically improbable.