I'll try not to use too many technical terms here, but...this is a simple matter of having your gain structure all F#@Ked Up.
I have a Tascam DR-100 and it is a pretty quiet machine all by itself with much better preamps than your DR-05, but there is a small amount of hiss at the low end when you push the audio gain up toward the higher end. The DR-100 uses the same high quality preamps that are found in the more expensive 4 channel, multi track recorders that Tascam makes. Over all, pretty good preamps. But any preamp is going to have hiss when you lower one input to almost nothing and then raise the other to near/or maximum. Whoever posted that video was not giving you the best advice. Welcome to YouTube, where anyone and everyone is an expert. That demo video may have worked for them in their particular situation, but that is a recipe for failure in most cases. Maybe that person's DR-05 just had a bit quieter preamps, maybe their inputs on their particular camera were cleaner than yours. There are lots of tiny, little things that go into audio that aren't always the easiest to replicate from set up to set up. Especially when you are talking about something like noise floor (this hiss you are describing).
What you really want to do in your situation is play around with it some more. Raise the input to the camera a bit more and lower the output of the recorder a bit. Bringing both devices back toward Unity (the center of the range for both devices). Whenever you have two devices set to radical extremes the way you do, bad stuff will usually happen.
Also, move closer to your sound source. People expect too much from mics sometime. Proximity is the friend of microphones. Get closer if you can, this will help you to not have to raise the input gain.
But then again, you aren't starting off with the best of the best. The DR-05 isn't as expensive as the DR-40 or the DR-100 for a reason. They put better stuff (preamps and circuits) as well as more features in the higher end recorders. And your T3i (600D) also isn't the top of the heap. So maybe you are asking too much from too little?
Maybe it worked in the video you saw, but then again, maybe it's the room that you are recording in as well. Every room or environment has it's own ambient sound. Refrigerators hum, furnaces blow and whirl and lights sometimes buzz. All of that is background noise that on a daily basis we tend to not notice and our brains let blend into the background and we don't pay attention to it. But those same sounds are also being picked up by your mics and that adds to the noise level. Usually that is something you don't want in your recordings. Professional sound people work hard to get rid of as much of that stuff as possible when working outside of a pro sound stage or recording room. Take a look and a listen to that as well when you record.
My last bit of advice would be this: Why not try recording only to the DR-05 and sync in post? Its really pretty easy to do and you'll probably end up with a better recording anyway.