In scenario that you are describing, you are comparing two means. You are doing so by looking at their difference if it is different than zero. In your case, since the means are exactly equal, you know that their difference is exactly zero. Hypothesis test appropriately returns $p$-value equal to one, so you cannot reject null hypothesis because obviously $p = 1 \not\le 0.05$ (or any other threshold value).
However this is something that you knew already before conducting the test. Think of it in terms of confidence intervals for means of both groups. No matter how wide or narrow would they be (i.e. how uncertain would you be about your estimates) they would always cross since the means are the same and the intervals are centred around means (that is true also for unsymmetrical intervals). Hypothesis test would not tell you anything more than this.