This is partly correct.
Like witchunt has said its most probably the CSP (Customer Splice Point) where the fibre from the hardware in the chamber by your phone pole if you have one then to your wall of your home.
The fibre then goes into the CSP where it is joint to another fibre going through your wall where it will be connected to the ONT (Fibre Modem) inside your home.
You are aware you can choose from a range of CSP Box colours, I think there a Grey, Brown and White, there might be more, but I have only seen those colours.
I chose the one with the nearest colour that matched the brickwork of our house wall.
You can also tell them where you would like the CSP Box to be placed, within reason that is.
I also asked them to place mine the other side of our bay window due to I wanted the internal hardware that side because of the power socket was that side and it would be easier for the routing of the network cable.
So where you said the BT Engineer said that they would have to dig up / lift slabs etc in your front garden, I assume you have no Phone Pole and everything is under ground?
If so this part might be true if there is not enough room for the fibre cable to be blown down.
But you can still choose the colour of the CSP Box.