Answer:
Yes- this is very true.
There are bacteria in sea water that actually consume the oil. On calm water, oil may create a very thin film on water (like engine oil leaking from a boat) and not cause any significant environmental damage. If the area is small, some animals may avoid the area where the spill has occurred.
Oil may be dispersed by wave action, and the small bits of oil may not to dilute to harm sea life.
In relation to the BP oil spill, the area became so large, that it was difficult for birds to avoid the spill. The impact on many animals is given in the related link.