"Is ancestry saying that we are indeed related to every match as has been suggested by some?"
What they are saying is that the number and size of the segments that you share with these people is statistically similar to those shared by individuals with that degree of relationship. They try to balance the possibility of missing a real relationship against that of giving you a false match, and that is more difficult the smaller the segments.
The technical term for this is that when segments are shared coincidentally they are called "identical by state" while when there is an actual relationship they are called "identical by descent." Unfortunately, in order to determine which is the case you have to do independent research for additional evidence.