According to the quote you provided, they only ask for a translation of the diploma, done by a trusted certified third party (specifically, the Hungarian National Translation Office). That is acceptable, and pretty much risk free.
For other details, you need to contact the company directly (possibly the HR department) to ask for details. Normally, for companies, copies are enough.
The specifics of each company are... aaa... specific... to each company. We cannot help you there.
Usually a simple copy of the diploma is enough for most companies. However, if the languages are very different (the language of the company and the language of the diploma), or even worse, they use completely different alphabets, then some translation is mostly mandatory.
My own example: at the company where I work now, a copy of the diploma was enough. Actually, it was a copy done with a smartphone, so not even a very good quality copy. They did the translation internally, aided by some online translation services, and asking me questions for the details that were not understandable from the automatic translation.