Without knowing the exact model of the Mac & without actually being able to see & examine it personally, it is hard to say. A bad Logic Board is definitely a likely part to replace. With 2016+ USB-C Macs, the I/O Boards are also a likely option (2016 & 2017 non-touchbar models don't have I/O Boards...so it would be a Logic Board). The other possibility is a bad Battery. I would need to trust the person who physically examined the laptop...it is possible the examination or their service diagnostic revealed the problem was most likely a defective Logic Board.
If you happen to have an Apple Silicon Mac with a Magsafe charger, then you could try charging the laptop using a USB-C cable instead of the default Magsafe cable. If that fails, then the Logic Board is probably the correct diagnosis.
At this point it doesn't seem like you have much choice in the matter if you want to continue using the laptop. If you have another Apple Authorized Service Provider available, then you could have them provide you a second opinion.