I don't understand your question. It is not unusual for the group median to equal a value in the data. Where it gets somewhat messier is in that the definition of "median" can vary and that can impact the estimations. Note that even though these p-values are called "exact" they are not the brute-force computations that we learned in graduate school (those approaches rapidly become prohibitive when the sample size exceeds 10).
Perhaps you could read the documentation referenced in
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ANOVA, or Analysis Of Variance, is used to compare the averages or means of two or more populations to better understand how they differ. Watch this tutorial for more.