The question that was actually asked is a little more involved:
"Is it OK to reuse the bottles that bottled water comes in? Sometimes when I am at a conference the bottled water they have is in a really sturdy bottle, and it seems like such a waste for it to be single use. But is it safe to refill it from the tap? My primary concern is BPA leaching into the water, but what about sanitation?"Let's overlook entirely the misinformation about BPA leaching from a PET water bottle . In fact the Grist article does catch that, but only after launching into a full paragraph about the horrors of BPA and then citing that discredited article from Bittner about other endocrine disrupters being in plastics of all sorts. But I'm fine with that, because even if the bottle is leaching an Unknown Nasty Chemical Attempting To Kill Us (UNCATKU) into the water, I would strongly recommend that the bottle be reused.
Assuming that there is an UNCATKU in the plastic, the concentration in the plastic is highest when the bottle is first drank from. The amount of UNCATKU that leaches out of the plastic into the water depends on two factors: 1) the concentration of the UNCATKU in the plastic and 2)the time that the water is in contact with the plastic. The higher the concentration of the UNCATKU in the plastic, the faster it will leach into the water. The longer the water is in contact with the plastic, the more UNCATKU will be able to leach into it. Given modern logistics, it is likely that the water in the bottle has been there for not just hours or weeks, but months and possibly a year or more.
For those reasons, I would suggest that if you are really concerned about the UCATKU, open the bottle, pour the water down the drain and then refill it before drinking. And for those same reason, I would recommend that you then keep the bottle and reuse it.
As the UNCATKU leaches into the water, the concentration in the plastic is reduced.  Every time the bottle is refilled and more UNCATKU leaches into the water, the concentration in the plastic is further reduced. If the bottle is refilled enough, it is conceivable that the bottle could become free of the UNCATKU. Similarly, when the bottle is refilled by someone, they are going to be drinking from it in short order, not months from now. Both of these factors which led to the conclusion of dumping the bottle out in the first place are now supporting reusing the bottle.
To close the Grist article out, the author comes up with a contradictory argument. The author further cautions against reusing the bottles because being "...moist, enclosed, and getting a lot of full-body contact with your hands and lips", they are bacterial breeding grounds. His advice: carry a reusable metal drinking bottle. This overlooks the fact that the metal bottle would also be "...moist, enclosed, and getting a lot of full-body contact with your hands and lips", but that's ok I guess since he is an anti-plastic advocate.
Worry if you want about the UNCATKUs hiding in plastic water bottles, but don't let that stop you from reusing them.
 PET is BPA-free because it was born that way. It always has been BPA-free. And I can't see that ever changing in the future. Making PET from BPA would be pretty idiotic.
 It is a little more complicated than this, as the concentration of the UNCATKU would be a gradient such as Fick's Laws would predict, and not constant. Correcting for that will not alter the overall conclusions of what I'm stating here, just the rate at which these events occur.