Having spent weeks in the rain with down; having spent said weeks in a single wall tent, I have many experiences.
There is rain, and then there is RAIN. Others have gone over and over keeping your pack dry and said clothes in said pack dry. Ditto on what they said.
Regarding Down, you NEVER actually wear down while walking/hiking as its WAY too hot unless you are WAY up somewhere high where its 0 or below, and even then... Your options are either move fast and strip down to keep cool, or move slow and DON't Sweat.
So, Down as a camping option, and keeping warm at belay. Is what we are really talking about. On belay, its simple, either you are running off the mountain because its raining which is damned dangerous as the rocks will be flying or its no raining and you are just throwing on said down jacket to stay warm. Generally while sitting at belay you won't be steaming your down coat. If you do open it up, and use jacket as a "bellows" to pump said water vapor out. If you plan on doing this in the snow, make sure its outter shell fabric is "waterproof" or breathable. Don't care which. One side breathable is fine by me. Turn it inside out to "dry".
Ok, Camping with down during extended RAIN. If its warm rain, we don't have a problem as drying out your clothes from sweat inside said sleeping bag is fairly straight forward as you won't have been wearing hardly any to start with. NOW, DON't GET TOO WARM as you will then SWEAT ADDING water to said sleeping bag.
Hiking in Cold rain, well to start with, hike fast, keeps you warm, wear not much, otherwise hike slow, don't sweat, because drying out is difficult. As others have said, if you are warm, YOU ARE WEARING TOO MUCH! At these high humidity cold temperature conditions, drying anything is difficult.
The worst I ever had with down was we had to pitch our squal2 on a 30% slope in the pickets in high humidity cold conditions and huddled for 2 days while it Poured, sleeted, snowed on us. Because of the awkward position of said tent our bags would slide down and we would contact the sides of the single wall tent. This got the toes of our bags wet, but otherwise wasn't too bad. One night on a regular flat spot after 2 nights of horrid conditions and they were dried out again by our body heat.
Likewise I have been in Coastal British Columbia in a modified Tarptent Cloudburst 2 for a week straight of solid rain. Our down bags remained perfectly warm and puffy. If you are too warm, open the bag if you are waiting out the rain.
If we are talking snow conditions, Down is fine as well. Get in sleeping bag with wet clothes, take wet clothes from sweat off put dry on. Put Vapor Barrier clothes on if they aren't already. BIG DEAL. Then warm said bag up, place wet clothes on top of your chest/around your chest and by morning they will be dry. Now, if your sleeping system is a "barely" this won't really work as well at temperatures close to freezing.
Temperatures close to freezing are the worse as the humidity can be extremely high. Low temps are far easier to deal with than near freezing and high humidity.
Been in a double wall tent once in a rainstorm, but only because someone else brought it along.
If you plan on wearing clothes while it rains, or sweating while hiking/climbing can't say enough about fleece/polyester and vapor barrier socks/gloves liners and even VB shirt/pants. VB you can overheat in so be careful. Fleece/polyester hold their loft while soaked because they don't absorb water like a natural fiber. Likewise they are not as warm as a natural fiber when they are dry though some of the new fibers are darned close!
Everything is Fleece/Polyester except my sleeping bag and Belay jacket. I see no reason to change this. Only reason I see for anyone to buy something like a Synthetic fiber BBag or Belay Jacket is because of cost.
For bombing around on the weekend? Can't beat the cost of synthetic sleeping bags. They are practically free. Heavy, but near free. As a kid, I took a big ol' tarp, twine, and a synthetic sleeping bag in a black garbage sack. I still carry a tarp quite often as its far more enjoyable to use in winter as it gives more area to spread out in during bad weather. Bring groundsheet as well along with a snowshovel for a snowcave.
PS. Diane, don't who "taught" your course, but they are utterly clueless. Probably pulling a giant CYA mentality that is so prevalent in today's lawyer environment as synthetic will dry out "slightly" faster than down. Claiming they are warmier when wet is Bull Pucky. Only thing warmer when wet is WOOL. CYA... Just like every damned hammer comes with a warning sticker on that claims, that you need to wear eye protection to nail a nail... Sure... Said instructors all have down bags I betcha as well.