In general, at least from my experience, military medics are less aggressive in starting IVs than civilian paramedics. (I used to be both). Military medics also vary widely in skill level and experience levels. Many haven't seen anything but blisters or sick call time stuff, some have spent tours in hell and know more than some surgeons about trauma. The SF medics have at the least done some time in an ER and handled a goat that took one to the chest.
However, I think you'd agree that once she started vomiting, they undoubtedly gave her IV fluids off-camera. That solution she drank was immediately puked.
Which brings up a point guys, sip that water once you get severely dehydrated. I've seen plenty of people in the desert do exactly as she did, drink too much and vomit. You're worse than you were before the gulps of water.
If you don't have an IV remember the rectal route, but even cooling the person off (water to the skin doesn't have to be potable water... could be urine even) may help get them to the point of being able to sip some orally. You can also hold water in your mouth without drinking it.