There has been a lot of emphasis on QM when detailing events here. Firstly, it would be beneficial to examine the foundations to modern physics, which are solidly hinged on mathematical pretexts that show significance when relating to various physical phenomenon. Quantum mechanics dwells on mathematical significance as perspectives. But that is not to say, that physical aspects to such measurements can be discounted, or misrepresented in a qualitative analysis.
The waves representative to particles mentioned herein represent radial probabilities, that are cumulative in a sense; rather than measuring electron densities at various points, the objective is to analyse the radial probability which takes into account the cumulative probability of an infinitesimally small volume at a distance r from the center of the nucleus, extended 3 dimensionally over a region encapsulating the nucleus at that distance. This eliminates the need to define the precise location of the electron, and thus, extends the uncertainty to a larger region by focusing on the probability distribution in the region. Hence the observation of the uncertainty principle.
All of the above remains valid so far as measurements and analyses are concerned. Ultimately, there is that certain electron in n=1 and n=2 and so on, and based on the probability distributions, these particles can exist at the same place, but probably at different times, if one is to observe other principles associated to the state of the electron.
Thats right; electrons do have definitive positions at a given time. The uncertainty principle governs measurements only, and is a correct one; we cant measure the position and momentum of an electron precisely, all at once.