I don't know about water heaters with recirc pumps, but it makes sense to me that the recirc pump is separate from the water heat, even though it might be attached. If you're getting hot water, although it may take a minute, I'd refuse any attempts at them replacing the water heater and contact the Home Warranty company about deceptive sales schemes by the service man. At this point, I'd like to think that you're safe, just inconvenienced.