Just because the poop isn't soft doesn't mean it's not coming out fast, so don't write off what she's saying yet. She could be having a reaction, sensitivity or adjustment period.
Has she been constipated recently? Has she been sick recently? Has anything in her diet/environment changed recently? New cleaners, new detergents, etc can cause reactions in the digestive system. Drinking more liquids, any extra mucilage in her diet (okra, flax, etc), more ferments/pickles in her diet, maybe more fruit than she's used to eating, higher % of raw veggies in her diet. . . all of these tend to speed along the elimination process and she may need extra time to adjust and learn how fast she needs to get to the toilet.
Also consider possible emotional stressors on her.
When she has an accident, try to not show your disappointment and frustration, but talk to her gently and find out how she feels when she has an accident. Also see if she knew she has to go, but was delaying it, absorbed in what she was doing or if she suddenly needed to go (if it's the latter look for a possible reaction to something in her diet/environment). If her BMs are fairly consistent (ie morning/ evening/ etc) try to help her predict when she'll need to go, so she can "plan" on a longer potty sitting (ie take a picture book or something to keep herself occupied for a few extra minutes instead of rushing back to whatever she was playing with before).
As far as trying to take care of her pants herself goes, it sounds like she is reacting to your disappointment that she didn't go in the potty. So your best bet is to gently explain to her that you want to help her get over having accidents in her pants and figure out why they are happening and find a solution that will help her avoid them in future. When she tries to clean herself off, remind her that you WANT to help her clean up when there is an accident and she doesn't need to be embarrassed with you because of it.