There was an ad last sunday that stated "We gladly accept Competitor coupons"
However, this is not totally true in it's entirety.
Here is an excerpt from an email from Walmart clarifying what they announced publicly:
Walmart will continue to accept all valid manufacturer and print-at-home internet coupons with a scannable bar code. In addition, Walmart will also match the price listed on any valid competitor coupons that include a printed retail price for a specific item (e.g., $2 for a 24 oz. bottle of Clorox)."
Example: You have a coupon from Target for $3/1 bottle of Dial soap - This will not be accepted.
You have a coupon from Target that says 3 bottles of Dial soap for $3 this will be accepted.