From memory (way back in the dark ages), when Ibuprofen first came out and was a new fangled drug only produced by one company, the only version you could get was Brufen - like until recently, you could only get Humira, but now you can get Adalimumab under several names as the patent has expired.
So the nurse wasn't wrong. And before NHS rules meant doctors had to prescribe generics under the active ingredient name to save money, many would simply write the brand name, as it is inherently easier to say/remember/spell (which is one of the reasons brand names are chosen by the companies in the first place).