They could for a number of reason.
If the car is very dirty, for example, some heavier dirt is likely to be on the paint; if its not removed properly before (with a water stream for example), when the dirt gets "brushed" the brushes will move the dirt around possibly creating small scratches all around.
On an old car (or any car with a weak paintjob) the brushing could be too strong and infact ruin the paintjob by creating small scratches or removing small parts of the paintjob in dangerous spots (corners for example).
Also, it can happen that if the previous car was very dirty, some of the dirt remains on the brushes, and again it can lead to dirt being brushed around and scratching the paintjob. Sure, we are talking about very small scratches eventually but every run they become more noticeable, especially under sunlight.
i'd say that type of wash is okay if the car is not so dirty and you know a reliable washer. In your case, if your car gets reasonably dirty (not wasted but dirty enough to have a wash) over a week you should be able to use machine car washes. Examine the paintjob closely afterwards and if you start noticing small scratches then stop immediately.
Remember that scratches are far more noticeable on darker and metallic paint.