Much has been made of the apparent capacity for creativity of generative AI. However, as research expands the knowledge base regarding the capabilities and performance of this technology, the prevailing view is shifting away from "AI is creative" and towards a more balanced model of Human-AI co-creativity. Nevertheless, even this paradigm may be impacted by untested assumptions: for example, that generative AI will boost human performance on idea generation tasks. To test that assumption this study primed subjects with lists of words purportedly either from a human or from ChatGPT, and of varying degrees of creativity. Subjects then completed the Divergent Association Task (DAT). The results of this study found no evidence of any difference in divergent thinking resulting from either the source of priming (Human/ChatGPT) or from the level of creativity of the priming (low, typical, and high), with one exception: a low-creativity prime, believed to be from ChatGPT, resulted in lower scores on the DAT compared to other priming conditions. A subsequent regression analysis supported this result, finding only the perceived creativity of the prime to be a weak predictor of DAT scores (in addition to the expected trait of Openness). The consequences of these findings for Human-AI co-creativity are discussed.