They would'nt be making and selling 0.060" oversized pistons if block weakening was a major issue. Your machinist probably has easy and cheap access to virgin blocks thru his contacts for when he needs one, and therefore could not understand why someone would want to go 60 thou over. I guess because it's because you're not made of money right? It's also probably an ethical issue for machinists and he's probably just protecting his own reputation. If you're really worried you can always pour block hardening compound into the water jackets. The piston manufacturers would have feed back records on going 0.60" over and you can always give them a call for a different point of view.
Being in the trade you soon predict the verdicts when you send something out. Every time we sent radiators to specialists for a flush we get a reply that the cores have cancer and require a recore. But after they patch up the old cores due to the customers lack of funds the radiators miraculously go on to out last the car! The world's full of drama queens.