I call this the difference between SAY & PAY.
People SAY all kinds of things. Until they PAY it means nothing. If you got the message in the gray box at the left side of your Inbox from Rover to Accept or Decline the booking it means they did PAY. Without that step anything they SAY does not constitute a booking and they would not be responsible to pay in way.
This is all part of the Owners shopping process. Some Owners use non-response as a way of letting you know they did not book you. Rover encourages Owners to contact multiple Sitters and once they select a Sitter they are under no obligation to 'release' the other Sitters.
To protect yourself from losing other possible bookings for that time frame it is important to Archive the request. There is even a reason of "Owner did not Respond" as a selection for why you are Archiving the request.