I just received some 10K .1% precision resistors from Digikey (part number PTF10KECT-ND). Unlike all their other passive components, which come in a normal plastic bag, these came in a metalized bag with a yellow seal that warns me that they're "electrostatic sensitive devices". They're kidding, aren't they?
I wouldn't discount it. Precision film resistors rely on laser trimming or very fine and precise film control. Both of which could lead to local film breakdown under high current.
Edit incorporated from comments:
Designs requiring a 0.1% precision resistor, or even two or more such resistors in ratiometric arrangements, would typically be much more sensitive to value change than less precision-dependent designs, thus it's a bigger concern: If one resistor in a set gets changed by ESD, the rest of them wouldn't be changed by the same amount, so nasty and mysterious problems will ensue.
If you think about it, ESD basically entails extremely high voltage ripping through the resistor, heating up what are somewhat thin regions , breaking dielectrics, etc. For anything that's precise, that's bound to affect it. Components are not always destroyed by ESD outright. Precision Op Amps, for example, when exposed to even low amounts of ESD can change their parameters such as offset voltages. Same with the precision resistor.
The best approach is to ensure you're properly grounded when working with those components and keep it in those bags.