Matt tells the hunter that he's ridden 100 miles since early that morning. This isn't believable. Riders typically travel around 20-30 miles per day on average when considering the need for rest, food, and water breaks for both the horse and rider.
It's hard to believe that Chester could walk the ten miles from the woman's house to Mingo with that game leg of his and keep up with Matt who stood at six foot seven.
It was very unwise of the woman to volunteer to Matt and Chester that her husband was away and probably wouldn't be back until the evening of the next day seeing that they were rank strangers to her. Matt hadn't told her yet that he was a US Marshall.
Matt told the injured hunter that they couldn't take him but they would send somebody back for him. But they never did. They forgot about him.
Matt and Chester set off walking the ten miles to Mingo without carrying any water with them. And they didn't ask the woman for any.