Broken phone

So my phone fell from my pocket and a car went over it, now the display and back panel is broken and also it keeps shutting down, I went to the service center and they are saying some IC on the motherboard is broken and at the service center they don't do the IC level work so it has to be replaced whole and for IC level work I will have to take it somewhere else. So, I asked if I could get my data somehow, but they said that first, we will have to fix the motherboard issue, and only then will the data be recovered. Is it true?