In popular media, and even in introductory books it is common to say that quantum objects are characterized by the non-intuitive notion of being in two or more eigenstates at "the same time".

An example about quantum computing (http://www.newsweek.com/quantum-computing-ibm-580751)

While traditional computers put bits in 0 and 1 configurations to calculate steps, a qubit can be a 0 and a 1 at the same time.

Isn't this definition misleading to the public in general? For me, superposition is not about two or more eigenstates coexisting at the same time, it is just a physical phenomenon that is mathematically convenient when we are dealing with probabilistic systems.

I am aware there is a lot of controversy even in the philosophical interpretation of quantum mechanics itself, which is not my focus to discuss the various interpretations here.

So, based on the grounds of quantum mechanics, is it correct to say that "eigenstates" "coexist" at the same time? Is the media and the common sense incorrect or is it just a convenient naïve approximation?

EDIT

Based on the discussions, I just rewrote states as eigenstates, to make it clear that I'm not saying that quantum systems "are in two states at the same time" as I'm aware a quantum system has only one state and it's well defined.

Coexisting refers to the notion of "many things happening at once before the measurement in the weirdness of QM world", as I think that is the common idea among laypeople.