Actually it's not fake.. and it's not Dr. Pepper's fault either.
It is the capsule part of a pill. My G/F is one of the senior Chemists for Dr. Pepper Snapple group and runs into this sort of thing all of the time.
Person washes down the pill with the first sip.. it gets backwashed into the bottle. Hour or so later, the capsule part absorbs the liquid like a sponge and expands. Normally the stomach acid will break the capsule down, but soda (as acidic as it is) is nowhere near as bad as stomach acid.
The thing that irks me is that the TV station never even bothered to contact Dr. Pepper on this (if they had and DrP didn't respond, they would for sure have made mention of that in their newscast... "Dr. Pepper refused to give any kind of comment on the situation"). I know for a fact because one simple phone call would have explained the truth to the news people, and that wouldn't make for a very good story, now would it?
If you take the time read the comments you might just be disgusted with what you see.. droves of people who are willing to believe everything they are told on TV regardless of its accuracy.