I think if you want to give a professional treatment and use the CACI to its full potential then it's paramount that you do the training with CACI.
Obviously no insurer will cover us without our electrical training( though I know of people who think they can do the equipments own training with just a level 2 and then be insured, this is simply dillusional of them)
I don't think we HAVE to do each piece of electrical equipments own training to be insured however if you're intent on using it then I would give your insurer a call.
In house training from staff already trained is ok, but not the best way forward, I mean, no disrespect to your friend who taught you, but just say she wasn't doing things properly? You could have been taught incorrectly( even if was a slight error) it does happen a lot in salons though and if you feel confident that you were taught correctly and the insurers say its ok,plus you can get all sundries then that's up to you.
Personally i would Get yourself off to train correctly in the use of that particular machine and then you can proudly show off another certificate and have the knowledge which is crucial to each piece of equipment, not to mention giving clients the satisfaction that you know your stuff.
There's always the other issue of clients maybe asking you something that you were not taught from your friend, and this would put you in a compromising situation being as it would more than likely have been covered in your professional training for CaCI. Hth