That actually IS the case if you work for PepsiCo. I was there, working a freelance job. I went to take a swig out of my bottled water and my boss almost went nuts, making me toss out the bottle before anyone saw it.

The brand, which might have been Dasani, I don't remember, was bottled by the Coca Cola company. Oops!
I found out, that when hired, each PepsiCo employee has to sign a form stating they will not buy, own, use, carry, etc. any products by their competitors. Furthermore, if their car is searched in the employee parking lot, or they have a family picnic and Coca Cola products are in their car or at the picnic, they could be fired.
PepsiCo employees are representatives of PepsiCo even in off duty hours.
I'm sure Coca Cola has similar employee rules.