Does a grayish/brown color indicate that raw whole-muscle beef has begun to spoil?

Not necessarily. When exposed to air, whole-muscle beef a may undergo discoloration and remain perfectly suitable for consumption. Unless product packaging is infused with carbon monoxide, all whole-muscle beef eventually assumes a grayish/brown color.  Consumers should note that  CO packaged meat will not change color at the same cooking temperatures as aerobically packaged meat, so a meat thermometer is essential to confirm that the meat is cooked to a   proper temperature.  Because color doesn't necessarily distinguish a fresh steak or roast from a spoiled one, it's always best to cook or freeze meat within 3-5 days of purchase.
 
Source(s):
USDA Fact Sheet "Beef...From Farm to Table"