I read in the comments: It seems to be false claim. This is far from being consensual. You have many publications claiming that this is true, including very recent ones, eg this one: The phyllotaxis of the model plant
Arabidopsis thaliana follows a Fibonacci spiral, the most frequent phyllotactic pattern found in
Many publications propose models to explain this phenomenon, eg this one (published in 2011).
This book chapter by S Douady who wrote several papers on the subject might interest you (the last page is missing but all the models are fully described).
PS: Nice video with lots of examples, no explaination or modeling.