The operative issue is whether the meat was handled properly after cooking, i.e., cooled before being packed for storage, not cross-contaminated by being placed on a dirty cutting board, that sort of thing.
Assuming it was handled properly there are two major issues of concern, concerning pathogens. First, if the meat was handled by hand (breathed on, coughed near, etc.) one can assume contamination by Staph. aureus (it's just too common and ubiquitous). This is the concern with proper (and fairly quick) thorough cooling (food packed warm, especially if thickly packed, stay warm for too long in the fridge).
Cooled properly and fridged or, better, frozen, Staph. does not grow. Staph needs warmer temps and some time to grow to the level it needs to produce toxin. So, cooled correctly and Staph. is a non-issue.
There are other possible pathogens that could develop on the meat if cross-contaminated after cooking (the dirty cutting board again, or handling raw foods before handling the cooked meat without adequate handwashing). The majority will not grow at cold temps either - except for Listeria. Were Listeria present on the meat before cooking, cooking would have taken care of it. Were it contaminated after cooking, outgrowth could occur at fridge temps.
But Listeria would be taken care of during reheating.
So, were the meat handled correctly after cooking and during prep for storage, as noted above, I see no reason to be concerned with food borne illness.
I have had food poisoning many times over the years. Yes, very unpleasant. However, 'shelf life' - in most cases - is about quality, not potential pathogen contamination. Remember, food pathogens have no odor nor flavor and cannot be detected by taste nor smell. If you smell something or feel something (like slime) it's not going to taste very good. Odor, slime and off-taste are caused by spoilage bacteria (and mold, in some cases). Microorganisms that cause food spoilage are not known for causing illness.
Were it me, if the food in question was possibly too long in the fridge but smelled and felt fine - and it was something meant to be reheated - I would, reheating thoroughly. (I would not taste it first.) Were it something not meant to be reheated I'd probably pitch it, if at all questionable.
My 2.
