If the carer has concerns, then she needs to alert her supervisor, who can request a review of her support plan with Adult Social Services, including a referral to assistive technology if appropriate.
She absolutely should not be encouraging people who are strangers to her to be involving themselves in the vulnerable adult's support. She doesn't know you from Adam! You could be capable of anything.
In my experience working with vulnerable people who live on their own, I would keep a wary eye on non-relatives who hang around. (And quite often the relatives too) Do you know how often people who live on their own are abused, robbed, or tricked into signing things? It's not nice to have to view everyone with suspicion, but it becomes necessary.
Out of curiosity, how did you find out that the woman was injured and on her own for 28 hours? Was it from the carer? The woman has a right to dignity, privacy, and confidentiality from her carer. The carer shouldn't even be telling you who she is visiting, or anything else about her client.
Equally, if you do become involved with checking up on her, offering to get shopping, etc. social services can view you as a form of "natural support" that justifies not increasing the woman's care package.
It's not just a matter of complaining to the company that she was rude-- the carer needs better instruction on how to handle her concerns appropriately.