While I agree in general, you know what they say about never say never.Sorry, but I find the idea that ANY modern digital multimeter can destroy ANY integrated circuit to be absolute nonsense.
I've worked with IC's that, because of the performance requirements, had zero input protection on the detector pins, were quite low impedance (they were current-mode inputs), and had circuitry that would be damaged by input currents exceeding 100 uA. They were a royal bitch to work with.
Even so, I'm pretty cavalier (more than I probably should be) about handling CMOS chips, including most of the ones I've designed, and don't think I've ever damaged any -- you never know how much life you've taken off one or how much you've affected it's performance by careless handling. We HAVE had chips that have gotten zapped and destroyed by ESD and I think some of those were due to careless handling during extremely dry conditions (and I'm pretty careful about strapping up when the humidity is low), but those events were rare.