Some devices can be very sensitive to stray conduction paths. For example, an ultra-low-quiescent regulator might have a multi-meg input impedance on its feedback pin. If a combination of board contamination and humidity allowed even 0.1 microamp to leak from the feedback pin to ground (equivalent to a 10M or so parallel resistance) that could cause the output of the regulator to be significantly higher than designed, potentially causing damage to the circuitry being supplied.
I'm not quite sure how such a thing would be a problem here, though, since it would take 100uA of stray current on an input to cause erroneous operation. Further, while dust contamination could cause overheating of a metal-cased or heat-sinked part, I really wouldn't think that would be much of an issue with a plastic-cased DIP.
Could the warning perhaps be boilerplate that appears in many data sheets, and is more applicable in some than others?