I think you will find they were wrong. I am not familiar with this box but most dual-tuners I have seen simply mean that you can watch one program while recording another. In my experience they actually output ONLY one channel at time and you cannot access the second tuner directly.
I may be wrong and there are 2 sets of outputs plugs on the back ? Maybe marked TV1 & TV 2 ?
Later: Just checked the datasheet and no, there is only a single output. You need to go back to the store and ask them to explain how you can watch 2 different things with only one output
If you have the Slingbox PRO HD, you can take advantage of the internal tuner. You only need to set a splitter on the coaxial cable that comes from the wall.
You will send two lines from the splitter: one goes to the set-top box and the second one goes to your Slingbox coaxial input. This way, you will be able to get the connection without affecting to home viewers since there will be two available signals: the first will provide you with all the channels you get through your cable box and the second one with the basic cable service channels.
Regarding the Motorola DCX3400 DVR it is a dual tuner that only allows you to watch TV and record at the same time. The "other kind" of dual tuner boxes are those that have the TV1 and TV2 video outputs on the back. These particular models will allow you to install the Slingbox in such way that the home viewers will not be affected if you connect to your Slingbox. Why? Because you will connect the Slingbox to the TV1 output (for Infra Red signals) and TV2 output (for Radio Frequency signals) to your set-top box. This specific connection layout will allow you to "split" the TV signal without affecting each other (you and the home viewers).