The Flight Training School are equally responsible as they should be ensuring that their staff are legal to work in the job position and also have the relevant Visa to be employed in the US.
Some flight school's do not care. There are multiple out there which are employing staff illegally and you only have to ask around to see which one has recently been closed down for doing so. Some management simply bump around from school/company to school/company - or even start new companies/schools after the one their at currently fails.
Insurance companies will be interested post accident, but post (hopefully there never is a post) and if they even catch on to the fact that the instructor wasn't appropriately qualified.
The CAA tend to always "allow" hours when ever there is an issue such as this.
The CAA can make your life very difficult and I would not advocate not complying with a standards document, as stated they can refuse licence issue or to accept a test (ie Standards document 3 / 19 for RT or some other issue there)