Some of HAL's early interactions with Dave are kind of sweet, particularly when he's complimenting Dave on his drawing. It's quite possible that HAL saw Dave as a friend during this time.
It's also possible right before he was completely shutdown, HAL played the pre-recorded briefing to Dave so that he could continue the mission.
But then again...guess what happened.
Floyd may be a cold spin doctor at work, but he's clearly close to his family. When he calls home, it's just to say hi, and when he apologizes and explains to his daughter why he can't be there for her birthday, she takes it in stride, and he promises to make it up by getting her a nice gift. (In a deleted scene, Floyd was shown calling a store near his home; he did indeed get his daughter a bushbaby.) The big joyful smile on his daughter's face at the end of the call says it all.