Yes, in the sense that you understand the "Why does this happen?", we really don't have an answer.
That an electron emits a photon is an allowed interaction in the underlying quantum (field) theory. This process has a certain probability to occur. And that's all we can say about it. As far as we know, there is no "trigger" for the emission, it is truly a random process occuring with a given probability.
To hope that there is a theory that does away with this kind of probabilism is to hope that there is a theory of hidden variables. Indeed, at least one interpretation of quantum mechanics, the Bohmian, is such a (nonlocal) hidden variable theory that would deterministically predict when and what happens if we knew the initial state of our system perfectly - this theory explains the observed probabilism then by our ignorance of the system, so that its predictions do not differ from a "truly probabilistic" interpretation.
Furthermore, Bell's theorem states that any theory that agrees with quantum mechanical predictions is either non-local, or has no unique predetermined measurement results (isn't realist). This means that you cannot ever get a theory that answers our questions of "Why?" as we wishes it did, because every theory that predicts unique results violates the idea that stuff can only influence each other at the speed of light, and every theory that plays nice with our relativistic idea of causality has no predetermined measurement results to speak of.
Therefore, it is indeed true: We have no idea "why" the electron emits a photon, and it is highly unlikely we will ever be able to say more than that it simply does. (This should not be surprising: We all know that "Why?" is an annoying, infinitely repeatable question. We also know that human knowledge is necessarily finite, so there will always be some point at which we cannot answer the why, and it is indistinguishable whether that is because we haven't found out yet or because there simply is no answer.)