Linguistic productivity, as evidenced by the use of words in novel contexts, is one of the most striking facts about human language. However, how abstract the knowledge that enables such productivity is remains unclear. We compare people's and computational language models' linguistic productivity in contexts where successful generalization depends on form-based information. We focus on extending the use of a novel verb learned in the active voice to passive contexts. We find people extend active to passive uses in a way consistent with abstract generalizations concerning linguistic form, even when no plausible meaning can be assigned to the novel verb. In contrast, large language models succeeded only when a meaning like an existing verb's could be assigned to the novel verb. We conclude that computational models' syntactic knowledge remains tied to the distribution and meaning of specific lexical items in a way that human syntactic knowledge is not.