I also think they do, but different dogs react in different ways. There are dogs out there who will even attack the weak, sick dogs.
Last time, when I fostered chihuahua in a really terrible shape, my rottie was often near her, licking her face, sniffing her and after a while chichi was looking for her "protection", she became very comfortable near her and thanks to her she started walking and following the rest of us (she wouldn't move from one spot for two weeks, even to do her business and it took her couple of months 'til she could go for a walk, and 4 months to get used to walking on leash).
Respect and you shall be respected. Animal is always right.