There is a slight difference in pronunciation that just takes time to pick up, and, yes, Danes pronounce their words like that... just like you take shortcuts in your own language, too. BUT you can use other clues to help determine the proper form. You would never say, "the girl eats strawberry." From the structure of the sentence you should know that it's a definite form. This doesn't work all the time since some sentences can use multiple forms, but for this sentence it's a good strategy.
I think it is probably pretty rare that anyone naturally says, in English, "The blank blanks the blank." "The blank is blanking the blank" is more natural-sounding, imho. I say this just so no one thinks they are equally to be used, even while noting that the lesser used is the closer translation.