Generic statements ('Tigers have stripes') are pervasive and early-emerging modes of generalization with a distinctive linguistic profile. Previous experimental work found that generics display a unique asymmetry between their acceptance conditions and the implications that are typically drawn from them. This paper presents evidence against the hypothesis that generics display a unique asymmetry. Correcting for two important limitations of previous designs, we found a generalized asymmetry effect across generics, various kinds of explicitly quantified statements ('most', 'some', 'typically', 'usually'), and variations in types of predicated properties. We discuss implications of these results for our understanding of the source of asymmetry effects and whether and in which ways these effects might introduce biased beliefs into social networks.