If the pans and surface are dry and there is no food splattering this would be permissible. This is the reason you can put different types of pots on a cold clean dry stove-pot (and if it is warm it is permitted since the heat acts as libun, see Mishna Brura 451:34).
If they are not dry and clear, one should clean/dry the surface before placing something else on it. This is particularly true in case the surface is not perfectly flat but has little holes or crevices.
Now a kitchen is a place where mistakes very easily happen so what you heard is very good advice: it is best to avoid a priori to put different types of pots on the same spot to avoid mistakes.
If it happened that one put two pots in the same place where either of the pot or place was wet, one should check with a rav if there is a real issue. The general guidance is that, for a cold surface
- if the liquid was cold and the pot was hot (say cold milk spilled on the table where you put a meat pot afterwards), the pot needs hagala (to be koshered) and the food is permitted (SA YD 92:7)
- if the liquid and pot were cold, one rinses the pot and surface in cold or lukewarm (not hot) water
- if the liquid was hot and the pot was cold, the food is kosher and the pot might be as well (need to ask a rav)
- if the liquid and pot were hot, the pot and countertop need hagala and the food is permitted if there is 60 times more food than the quantity of liquid
If the surface in discussion is hot (e.g., a stovepot or a hotplate) or near the fire, then everything becomes more serious and comparable to the hot/hot case above.
But again in all these cases it is very important to ask a rav in case of practical issues since small differences in the reality can have a significant impact on the halacha.
For further reading see The kosher kitchen pp. 167ff, here, there and the beginning of here.