S1 visa Substitute Teacher

Hi,
I read that the International Beijing School in Shunyi,Beijing are able to employ substitute teachers only if the individuals have an S1 visa. They have widely advertised this (Glassdoor, their website etc.). Is this legal? Or, have you heard of international schools being allowed to do this?
In addition, do you know if an S visa can be changed to a Z visa while in Beijing?
I was advised with a S visa to change it to a X visa you have to leave China.
Any help would be greatly appreciated.