Not sure if this is of any use, but when the tenancy was registered with the then PRTB, and then latterly the Part 4 renewal, names of all adults living in the house were required. Has the family not contravened the registered tenancy by inviting "visitors" to reside in the house on a somewhat permanent basis? I totally agree that it sounds as if there could be an insurance issue as RSI always ask for number of tenants etc..
This is a sticky issue as I am sure your friend will lose them as tenants if they are approached with a rent increase to cover the extra occupants etc... That said it might put her in a slightly better position moving forward. Now that they have been asked to vacate (and yes I would put it in writing), relationships have probably broken down a bit anyway. Highlighting insurance issues and original RTB lease might be the way to go.
I'm sure if the shoe was on the other foot the tenant would not be too worried about the landlords situation. If they were, all this would have been discussed and she would not have found herself in this situation now. Sometimes, good landlords can be totally taken for granted.