It's Important not to hit people with strollers

So we're having this issue where Abby accidentally hits one of us or throws something when we're not paying attention or falls on us or something like that and a good part of the time she really cutely says, "Oops, my fault, I'm sorry about that, that was my fault."

The other part of the time - I think when our reactions are stronger she says it wasn't her - the floor came up and slapped him or a similar sort of thing. I don't think it's a lie to get out of punishment, I think it's a lie because she feels so guilty and doesn't want us or herself to believe that she did it... scared of judgment?? I don't know. But I'm afraid other people will take it as a plain old nasty lie and so I obviously would like to curb her away from doing it.

Anyway, she gets irrationally upset (as if we are calling her a liar - which we aren't) when we tell her that, no, we saw her and it's okay but she did it.

The only idea I've had so far is to point out whenever I accidentally do something that "See, Mommy didn't mean to spill that on the floor, but I did, oh well, I'll clean it up." OR like when we were getting in the car with a stroller I couldn't figure out how to fold up so I tried to fit it in the back with Abby but when I closed the door on it it jammed into Abby's leg... So right then I told her how awfully awfully sorry I was and that it was my fault and I didn't mean to do it and I'm so sorry that I did.

SO we're on the way home from somewhere today and Abby rips a page in a book that we told her to be careful of and she says she didn't do it - it was just a pretend rip. And we started in on the whole taking responsibility even if it's an accident and it's okay blah blah blah. So this is how it went:

Me: Like remember when I accidentally hit you with the stroller? I didn't mean to do that, but I did, and I was really sorry and I told you that.
Abby: Yeah, you hit me with the stroller.
Me: I know, and I'm so sorry I did that. Did I say I was sorry?
Abby:Yeah. You shouldn't hit people with strollers.
Me: I know, it was an accident, I won't do it again.
Steve: So, Abby, you see? It's okay if you do something wrong, you just have to tell the truth about it. It's very important. Right?
Abby: Yeah, it's really important not to hit people with strollers.
Steve: Yes, but what else is important?
Abby: It hurt my knee.


*sigh*