Because of this "just a piece of paper" (as George Bush calls it) called the Constitution.
The courts recognize an exemption of the forth amendment for certain cases where the police either witness the crime being committed or have compelling evidence that the crime was committed and time spent getting an arrest warrant would potentially allow the criminal to escape or destroy evidence.
The exact rules for when police can arrest without warrant vary from state to state (and since you decided not to bother answering the mandatory question as to your state, we can't go further).
The answer to your last question, if I can understand what you are saying, is NO it doesn't matter if this is independent or coincidental with another arrest going on.