Unlikely IMO - especially in the forest. From images posted, the roads in the area in which she apparently planned to run are very narrow - I doubt there'd be any drinking facilities en route.
It strikes me as rather odd that she didn't take any water with her. Even though the temperature was cool when she apparently headed off, as a runner with at least some experience, she would probably have checked expected temperatures.
Even if she didn't, it's the middle of summer, and she was planning a longish run as stated at the dinner party the previous evening. Water would surely be a no-brainer.
Maybe she did take water. I suspect that it's been assumed that she didn't take water with her, based on the image of her with the doggy-poo bag. (Maybe she'd put any water bottle down while organising the doggy-poo.) JMO