Fressen as a synonym of eating is quite rude. You're right with your definition as to eat like a pig/animal. You would never use it in a formal context except when talking about animals. It's considered vulgar. Some people might use it with humans, but I wouldn't recommend doing it.
In other contexts it's okay to use fressen. Some examples:
Die Hausarbeit frisst eine Menge Zeit
Housework is consuming a lot of time.
Der Kopierer hat meinen Brief gefressen.
The copy machine pulled in my letter and destroyed it.
Der neue Bahnhof wird Unmengen von Geld fressen/verschlingen.
The new station will require a huge amount of money.
All the examples above use fressen in the sense of consuming something with the connotation of greed or excess. Verschlingen in these examples is a more formal synonym to fressen.
The following example, however, is a common idiom:
Den habe ich gefressen.
I don't like him.
The verb fressen is also used in more figurative ways:
Der Bohrer frisst sich in das Gestein.
The drill eats itself into the rock.
Finally, there's a verb that has been derived from fressen: etw. ausfressen. It's mostly used with children that have played a trick on someone:
Was habt ihr jetzt schon wieder ausgefressen?
In my opinion, the usage of fressen in your example isn't rude. A person can be eaten up by a disease or a bad feeling. Especially for cancer, this imagery is used from time to time. For example, you can say
Seine Gier frisst ihn auf.
It means that a person is heavily influenced by a feeling (here: greed) so that their personality changes gradually.