HEPA filters, airliner HVAC and COVID 19
The air that enters the cabin of an airliner usually comes from a mixing manifold, like e.g. shown here for the Boeing 737:

(Boeing 737 NG FCOMv2 2.31.7 Air Systems - Air Conditioning System Description)
There are three ways to supply air to the mixing manifold:

From the PACKs (Pneumatic Air Cycle Kits): these are the air conditioners on the aircraft, which are supplied by hot and high pressure bleed air (either from the engines, the APU (Auxiliary Power Unit) or via an ASU (Air Start Unit) on the ground). During flight, the engines supply the bleed air to the PACKs, which results in fresh air entering the cabin.
From the Ground PCA (PreConditioned Air) hose: here the air conditioner is on the ground (usually in the airport building) and it supplies conditioned air to the mixing manifold while the PACKs are still off. See also What is this tube connected to a 757 for?
From the Recirculation Fan: here air is taken from the cabin and the fan returns it into the mixing manifold. You can see the filter in the diagram in this related answer in front of the recirculation fan, which is the HEPA filter preventing the spread of a virus via the mixing manifold. Even in flight, some air is always recirculated to reduce the required amount of bleed air from the engines.

Your question seems to focus on the time where the aircraft has already left the gate (so ground PCA is out of the question), but is still on the ground. At this time, the engines are usually running, so they could supply fresh bleed air to the PACKs. For longer waiting times, the engines are usually switched off to save fuel, but the APU would be running to power the aircraft. The APU could then also provide fresh bleed air to the PACKs.
As the quote from quora you included shows, this bleed air is not always of the best quality on the ground. It can therefore be switched off by the pilots. The following picture shows the bleed air panel of a 737-800:

(Boeing 737 NG FCOMv2 2.10.2 Air Systems - Controls and Indicators)
At the bottom are the bleed air switches for the engines and the APU. When they are switched off, the only source of air into the mixing manifold is the recirculated air. So in this case, you are already running on 100% recirculation, which is then HEPA filtered. Since the air does not go through the PACKs, it is not conditioned though, so it will get hot and stuffy in the cabin.
The top row of switches on the panel are for the two recirculation fans. They can also be switched off, in which case no air would enter the mixing manifold any more. This would make the cabin even more uncomfortable on the ground and of course also remove any HEPA filtering.