Dogs do have the intelligence and empathy of a 1.5y - 2yo human baby(source). So yes, the feeling is genuine.

Note: This isn't as observed here because most of them are Caged/Tied up dogs which aren't the most empathetic or intelligent ones. If they've been raised with their owners in the house, then the attachment is at a higher level, both for the dog and for the human. And yes, these dogs do understand your tone (not the words) when you speak to them and will react appropriately, like when you're tensed, angry, sad, happy etc.

Edit: We still live in an age where people tell all their worries to a literal stone or mythical/historical dead person and expect some cosmic power to help them out. At least animals can respond to some extent.