How does a forest-dwelling dhutanga practitioner get food?
The page you linked for āraññika dhutaṅga seems to already have an answer:

A &quot;forest monastery&quot; is a monastery situated at least 500 (curved) bows lengths from the doorstep of a house situated on the remotest spot of a village.

This sounds like only a few miles away, so totally within walkable distance.

The bhikkhu who practises the āraññika dhutaṅga must fulfil several daily duties, such as performing his food collection by means of his bowl.

...

When the time has come to go collecting his food, the bhikkhu conveniently closes his robe, takes his bowl and proceeds to a neighbouring village in order to receive his daily meal. Before proceeding to the village, he puts into order all that which remains outside of his lodging and properly shuts down the door. If the path leading to the village is rough, he can tread it with his feet dressed in sandals. However, he must remove them and set them aside just before crossing the entrance of the village. He must minutely observe all sekhiyas. He enters in houses with attention and manages remembering his own location (in order to trace back the house of a dāyaka who invites him to come collecting his food at his home), he avoids entering while not collecting food or in case of emergency. He avoids being too slow or too fast while entering and going out of houses. When he waits standing with his bowl, he stands still neither too near, nor to far from the house. He never waits too long in front of a house. When his collection is completed, he doesn't go to people's house, without good reason. He doesn't waste his time into idle talk. He enters his forest monastery without delaying.
When he enters back his forest monastery, he conveniently performs all allotted domestic duties, such as the storage of drinking water for various uses, or sweeping. When darkness already came down, he lights up some oil lamps. So as to avoid any danger caused by animals, he catches up a stick for protecting himself. He tries to trace back the location of the stars and the four directions (South, East, North, and West) so as not lose himself. He pays attention to the calendar (regarding uposatha days, etc.)
If a bhikkhu who lives in a forest monastery has an unhealthy instructor or preceptor and the monastery doesn't receive any medicines (or medical materials likely to heal the later), he must take him to a village monastery, where he will easily receive all necessary cares. By doing so, the bhikkhu who practises the āraññika dhutaṅga should leave the village monastery before dawn so that he will have reached the forest at dawn time. If the state of health of his instructor or preceptor has worsened, he must remain in the village monastery for the sole task of looking after him. In this case, no worries for his dhutaṅga. The state of mind being the main element, the dhutaṅga is not broken.

So it sounds like visiting the village is allowed (and even required!) for food collection, and staying in the village overnight is allowed for emergencies.