Interestingly, had she been daft enough to go to court with it, she would have had to produce those EICRs as evidence of your "wrongdoing" (I'm assuming she was taking the line of "your EICRs were rubbish and therefore you're incompetent"). At which point, if you were certain of your ground, you'd be able to report the other electrician - to their competent person scheme if they were a member.
Even solicitors will try it on. Maaany years ago (with some friends) I had a computer business, and we used the services of a local solicitor while setting up the business. We never noticed that they hadn't billed us for their time. Roll forward a few years, the original business had failed (lets say, more enthusiasm than business acumen ?), and a couple of us had set up a different one. Then we got a demand from the solicitor for some money - a partner was retiring and they realised we'd not been billed, so they billed us and demanded payment. They soon shut up when I pointed out that we had engaged them as officers of the first company company (which had by now been wound up) and our current company was not liable for the debt - and threatened to report them to their governing body if they persisted. They would have known before they even asked for it that they were in the wrong.
PS - I've also used the statutory interest thing in the past, you'd be amazed at the reasons/excuses some companies can come up with as to why it "doesn't apply to them".