Thank you very much for your question and I will try to explain the open question:
First of all it is important to know in which environment the company is operating.
(1) As a maintenance organization under EASA Part-145:
Here the requirierend is clear stated in the EASA Regulation – The training and examination of NDT personnel shall be under the control of an National NDT Board (NANDTB) for the case a National NDT Board is established. Normally the NANDTB is approving an outside agency (Training school) or an inside agency (company internal). If no NANDTB is present the local aviation authority shall be responsible for controlling the NDT education and examination in this country.
(2) Design Organisation EASA Part-21 – here the training shall be established based on the requirements of the EN4179 but it is recommended to follow the procedure of the NANDTB of the applicable country. That means, the training shall be conducted at an NANDTB approved training school but in principle it would also be possible to do the training inhouse (own company training) if it is controlled by the National Authority.
(3) Organizations without Aviation approval – The responsible Level 3 of the company can decide if the training is done inhouse, our at an training school (outside agency). But be careful with the customer requirements. Sometimes they require training under the control of some Auditing organizations.
So you see, the answer is not straight forward and the requirements are based on the focus of your comapny.
Hope this answer is helpful for you?