This suggests to me that there is a subject-object relationship proximity issue rather than a possession issue.
...

Yet another example is "I'm going to town", although in this case if you said "I'm going to the town" you would cause confusion, and your interlocutor would probably ask which town you actually intended going to. But again, usually, you are referring to the centre of your current town, or if you live in the country you are referring to the nearest town, or at least the one you go to most often.

I just came back from a scene study class, where we worked on Brian Friel's 'Dancing at Lughnasa', an Irish play. The women kept talking about going into the town. It sounded a little foreign to me, and I kept wanting to omit the 'the'.