Does capacitor invert AC signal volatge
You may find it helpful to think of capacitors and inductors in this way during initial analysis of a circuit:


Inductors tend to keep the current through them constant in the short term.
Capacitors tend to keep the voltage across them constant in the short term.


In your capacitor circuit the initial voltage across the capacitor is zero so when the AC input signal "lifts" the left side of the capacitor the right side will follow. It will behave the same on the negative half cycles.

With the high input impedance of the oscilloscope very little charge will flow, the voltage across the capacitor will be close to zero and the two traces will be almost exactly the same. As you add lower values of resistance across the output you will see the voltage fall and the phase start to shift.