First, I have to apologize, because re-reading what I wrote, I have to say I was too loose with my language.
Where I said 'different phases being grounded at different times', I should have said 'each phase is _faulted_ to ground at different times'.
In a high resistance grounded system, you have a system node (the transformer neutral) intentionally connected to ground via the grounding resistor. Any other connection between any circuit conductor and grounded metal is a ground fault.
You can similarly describe solidly grounded systems an ungrounded systems. In general you have at most a single intentional connection between the system and ground; everything else is a ground fault.
Now consider a VFD with a ground fault on its output. Which 'input phase' is connected to ground? Which 'input phase' has the ground fault.
Let's start with an analogy: instead of a VFD we have a simple reversing manual starting switch, such as you would find on a small machine tool with a three phase motor. Imagine a connection to ground at the motor. Depending upon the FWD, OFF, REV position of the switch, that ground fault might show up on one or another phase, or might not show up at all (if the switch is open).
A VFD is really just a set of switches, continuously going from one state to another in a well defined electronically controlled pattern. Based upon which switches are closed and which are open, each input phase will in turn get connected to each output phase. Thus a ground fault on an output phase means that each input phase in turn has a ground fault.
In most common VFDs, there are two sets of switches: the input rectifier and the output bridge.
The input rectifier is quite dumb; at any given instant in time, the phase that is most positive is connected to the positive DC bus, and the phase that is most negative is connected to the negative DC bus. As the input goes through its 60Hz repetition, each phase in turn gets connected to each DC bus rail. If the DC rail voltage is high enough, there may be periods when there isn't a complete circuit between supply conductors and the DC bus.
The output bridge is controlled to generate the desired voltage and frequency. Each output terminal is alternately connected either to the positive or negative DC bus.
Each input phase is _sometimes_ connected to each DC rail by a closed switch, and each output terminal is _sometimes_ connected to each DC rail by a closed switch. Thus if there is a ground fault on the output of a VFD, that fault will _sometimes_ be connected by a chain of closed switches to each input phase.
Fault current flowing on the output of a VFD flows from all of the input phases, each at a different time depending upon which switches are closed.
I hope that my babbling on this topic is somewhat more clarifying than confusing
-Jon