Sharp probes ironically do far less damage to the PCB than dull ones. With dull probes, one has a tendency to push quite hard in order to make good contact, thus deforming the track/pad and potentially causing it to lift from the PCB. A needle-sharp tip only needs to gently touch the surface to break through the oxide and make good contact. A sharp tip is also far less likely to slip and potentially short out nearby pins or components.
This is the exact same reason that a poorly tinned soldering iron tip, too low temperature, and/or inadequate flux can lead to PCB damage - one presses the inadequate tool into the PCB too hard, in an attempt to get better heat transfer, and this deforms and damages tracks. Add the factor of heat, and lifted pads can easily result (especially on single-sided boards).