The concept of plant intelligence, as proposed by Anthony Trewavas, has raised considerable discussion. However, plant intelligence remains loosely defined; often it is either perceived as practically synonymous to Darwinian fitness, or reduced to a mere decorative metaphor. A more strict view can be taken, emphasizing necessary prerequisites such as memory and learning, which requires clarifying the definition of memory itself. To qualify as memories, traces of past events have to be not only stored, but also actively accessed. We propose a criterion for eliminating false candidates of possible plant intelligence phenomena in this stricter sense: an "intelligent" behavior must involve a component that can be approximated by a plausible algorithmic model involving recourse to stored information about past states of the individual or its environment. Re-evaluation of previously presented examples of plant intelligence shows that only some of them pass our test.