You're partially correct, but describing it in that way makes it sound like if you could "just look a little bit closer" the statistics would disappear, which doesn't happen. So it's more subtle than this. Fundamentally it's because QM doesn't use additive probabilities, but rather additive amplitudes which are complex numbers, and the probability is the square of the sum of these, so you can get interference between amplitudes. You can never get interference by adding probabilities.
In the dual slit experiment this is visible as you can't get the interference effects by summing the probabilities for "particle through slit 1" and "particle through slit 2" but rather you need to sum the amplitudes of the processes.
Working physicists (since 100 years) just do this, there is no practical need to interpret it further, but it would be cool if someone could figure out some prediction/experiment mismatch that does indeed require tweaking this!
In the dual slit experiment this is visible as you can't get the interference effects by summing the probabilities for "particle through slit 1" and "particle through slit 2" but rather you need to sum the amplitudes of the processes.
Working physicists (since 100 years) just do this, there is no practical need to interpret it further, but it would be cool if someone could figure out some prediction/experiment mismatch that does indeed require tweaking this!