I don't think there's many people that wouldn't say sorry in that situation!
I think I'd let it slide if she had said something like, "Oh no, are you okay?" and maybe helped her get up (if it seemed appropriate to) which would show she cared even though she didn't feel she needed to apologise. But to not even acknowledge is so rude. To be honest in that situation it wasn't on purpose but she was going backwards so it was her fault all the same, and I think an apology was appropriate, but whatever, if she had seemed like she cared or was bothered, the apology wouldn't matter so much.
The other day a little kid hit her face on Joni's swing at the park (OH was pushing). It was clearly not OH's fault at all because the child ran right inbetween him and the swing (she was 3). He tried to get back inbetween the girl and the swing but it just clipped her on the chin (didn't bleed or anything). The girl's dad was right there (we had been chatting to him whilst he pushed the girl's twin brother in another swing) so he picked the girl up and cuddled her (she was SCREAMING which is understandable). My OH and me were very concerned and we looked after the brother, got him out of his swing when he asked and I kicked the ball for him and cheered when he scored 'goals'. After about 5 minutes the girl was ready to carry on playing (although I think it ruined her time at the park because she had a tantrum on every single thing after that, which she wasn't doing before). But I don't think we apologised, since it wasn't our fault at all. I hope that doesn't sound mean of us. It wasn't like we just stared at her then carried on.
But that story is a bit different because in your story, the worker WAS at fault by walking backwards without looking (even though she didn't mean to cause harm) whereas in this one, there was really nothing we could do once the girl darted towards the swing that was coming towards her. Anyway, my point basically is that when people get injured or fall over around you and you are involved in some way, it's just being a normal human being to have some concern about the welfare of that person, whatever your thoughts on apologising in different situations is.