"...red meat..."
I would suspect that red meat eating would be a later development of a more "cultural" type than physical that an already meat digesting, longer living, and intelligent primate would turn to.
The creature that can eat fish that wash up or are grabbed from tidal pools has a wider food selection than the one who can just eat shellfish and are therefor less susceptible to food shortages and competition. The ones capable of properly digesting the fatty fish have even less competition and a wider range of places to live. One of them finds a crippled mouse and gives it a try. Soon its offspring are moving inland to "hunt" by intentionally reach into rodent dens the same way previous generations reached into crab holes. The progression of food sources, habitats, and intelligence levels just continue but the critical meat eating and fat digesting ability of this proto-humanoid is already present from earlier forms.
FTR. Lest some reader think Im trying to pass myself off as some sort of paleoanthropologist, Im not, nor did I sleep in a particular hotel last night, Im just trying to use logical commoners SWAG.
"I suppose it could. You can see here that our canines are rather atrophied compared to our existing more vegetarian primate relatives so Im not so sure theres a connection to meat eating with the canines."
The connection with canines and meat eating is that if you eat meat... you normally use canines. They cut and pierce the meat, making it easy to swallow and digest. Primates with an apparent canine set are going to be hunting and using those teeth as hunting weapons. Yes, some use tools, but there is a trend (IMHO) that the more ingenuitive the primate is, the smaller their teeth are.
This would suggest that intellect (and the evolution thereof) would compensate for a lack of natural tools. Either that, or we were built this way for simplicity's sake.
The idea of red meats being a "cultural" type over a "physical" one overestimates human nature. If I knew there was a rabbit in a bush, and saw a deer 20 paces off as well, I would try to take down the deer first. This isn't to say "look at me, I can eat red meat" this is to say "I can provide enough food for a while now. Thank goodness." It would be a need more than a development of culture. More meat for a social creature insures survival of the group, and thus the individual.