Usually when a motor is rebuilt for the first time, its cylinders are only worn .010-.018". Then the bore to .030" will straighten the walls back up because .030-.018 gives you a .012" cut into the maximum wear in the cylinder. Divide .012" by 2, and you're cutting .006" into each wall.
So if your motor is worn too close to .030", they may have to bore to .040". But usually you don't go from standard bore to .060" unless:
1) You're going for maximum cubic inches
2) You already bought a set of .060" slugs
3) There is a gouge in a cylinder
4) .040" pistons are not available (for particular app)
I don't know why the machinist would lie to you, he gets the same money whatever size he bores it. Unless he took a bad measurement, or thinks .040" aren't available.
On a related note, have the block decked .010-.015", because the oversize pistons sit a little lower in the holes.
good luck
chip