P-value Question

Hi,

At time 2:45 in the video, we see the output of the Dickey-Fuller test has a p-value = 0.41. The explanation of this was "This suggests there is roughly a 40% chance of not rejecting the null". From my understanding, the p-value indicates the probability of a Type I error or False Positive. Therefore, I would interpret the value as "there is a 40% chance of rejecting the null hypothesis when it is actually true". I am confused if this interpretation and the one given in the video mean the same thing or if I am misunderstanding the correct way to interpret p-values. Thank you in advance for any help!