Lo and behold, a family lives under that layer of grease. And things only get greasier with each passing day, as these folks continue to pour it into ailing automobiles on a daily basis. The "Filling Station," we find out pretty early on, is family-run, by the father and his sons. The women in the family (if there are any) seem to be steering clear of the grease trap. Signs of family and home trickle their way down the poem: there's a porch, some furniture, a plant, and even a pet dog. If this place didn't look like the site of a huge oil spill, it might look like a normal house and home. Almost.
The speaker is romanticizing the relationship with the young men and the owner of the station; they're actually not related at all. It was the speaker's assumption that the filling station was family run, just so she can make it seem nicer than it is.
The whole point of this poem is to show that even though this place is run down, a family lives there, so there's actually a lot of love and happiness.