Really? I'm sorry, but no. The phrase "no less shallow" - or heck, "no less <insert word here>" - indicates that comparatively, one is no less and no more shallow than the other. That they are equal in shallowness, or whatever word <insert word here> becomes. I can't believe I had to explain that. Please, stop.
If you think RDR is deeper, well, okay. I mean, sure, it had bounties that would pop up from time to time, just like random side quests, except there's less interaction to them than the Fable III sidequests. It's just go here, kill or lasso some dude, and then get all the way back to the nearest city while a big posse of respawning other dudes come run you down and shoot you, managing to keep up with you no matter how fast your horse was until you hit an imaginary line somewhere near to your destination. It's kinda like how cars in racing games can always still catch up to you and pass you, or how Call of Duty endlessly respawns enemies until you pass imaginary lines that turn off that area respawn. There was the occasional posse that would spawn and ride through town dragging some random schmuck by lasso. And it had people who either didn't talk or repeated the usual dialogue lines - forgive me, I don't remember which, it's been awhile - who'd run across the streets but could not be interacted with unless you felt like shooting them or something. But yeah, you're right, it had weather. And animals that ran around. And cacti. And a train. I like trains. I used to have model trains when I was a kid - big ol' board done up and the trains would choo-choo around. It was awesome. I think I even had some cacti on it. The animals didn't run around, though.
Fable's wandering husks are like RDR's wandering husks. Anyone who isn't an integral NPC is a wandering husk. Fable III's sidequests have more attachment. Fable III's environments change over the course of gameplay, while returning to a previous locale in RDR results in the same sidequests being present (like card games) and the same husks being around. But Fable III doesn't have weather, nor does it have cacti, though its underground monorail kind of gives the RDR choo-choo a run for its money. Like I said, no less shallow. Simply, the world is as immersive as the player chooses to invest himself or herself in it. Take me for example - I find myself more invested in the Dragon Age and Mass Effect games, and notably of late in inFamous, despite the fact that none of them are more or less shallow in terms of world ambience than Fable III or RDR. I just like them more. And really, as far as inFamous goes, I think Cole is more boring than dirt, I hate Zeke, and I'm tired of the townspeople running up to me every three seconds and saying the same things. But I'm invested out of fun factor alone, possibly, and immersed in pretending Cole isn't a giant stupid chucklehead.
Also, I did point out that RDR has better storytelling than Fable III. Did you miss that? I think you did, because it's not direct, so it must inhibit your ability to sniff it out. See, that would be an indirect way of mentioning a game's shortcomings. In this case, Fable III's. Thank you now. Yes, that's about the extent of my reply to your final paragraph, except to say that there being three full games doesn't mean it clearly works. More like we've had three full games because they sell enough to keep making them. The movie tie-in genre of video games doesn't work, but those things keep coming out of the woodwork like mice. And Alan Wake worked wonderfully, but we won't be getting any more full games of it, for whatever reason. Just a couple examples.
Thank you again for reading. Just slow down and try to see past the rage and see the words, please.