Mark, don't stop cross-checking (although it is less critical with an IFR-approved GPS, I suppose). Many is the time I thought I've been in good shape with DME, only to find the cross-radial not agreeing. Sometimes it's a result of having the wrong radial, other times it's a result of misreading the required DME figure, or having made an incorrect calculation.
Richard Collins has it right, with the caveat that technology shouldn't replace a pilot's ability to fly the airplane. Note, many airlines are making changes to their training/currency programs to ensure the pilots still remember how to fly the airplane.
Here's a practical case...take a pilot who is comfortable and proficient with hand flying single pilot IFR, versus one who, when all is said and done, really isn't able to balance the workload of SPIFR, working with ATC, briefing approaches, etc. As long as the autopilot and glass screens are available, the distinction is moot. It becomes a lot less moot when something fails (and GA autopilots are notorious...just see how many are placarded as inop), though, and you're back to hand flying with 'raw data'. Now we've gone from a seemingly academic distinction between the two pilots to one pilot living and the other one spiraling to their death. I don't think that's a sensational representation, either.
So, if an experienced pilot is using all resources available to him/her, that's smart. If a pilot is using the automation as a crutch (whether they know it or not), it's a problem. In the case of student pilots, heavy use of automation denies them the ability to hone those stick & rudder skills, as well as the ability to fly raw data. Check out this "Children of the Magenta Line" youtube video:
http://www.youtube.com/watch?v=h3kREPMzMLk (admittedly, I haven't watch it in full yet myself, but I keep hearing about it, and the name really does say it all).
In short, if you're using the automation for the right reasons, fantastic...that IS smart. It's a slippery slope, though, and the less experienced a pilot is prior to using the automation, it can be a case of "they don't know what they don't yet know." This is why in the 2nd workshop video, I rule out the use of GPS for the flight. It's not that I have anything against GPS, I love it. I just don't love how it's replacing certain skills which are critical to safe flight.
Note: all of this applies, btw, to real world pilots only. There is no "critical to safe flight" aspect for a sim-only pilot (I hate to make the distinction so bluntly, but I want to be realistic, and to remove the burden of training from sim-only pilots who aren't trying to build ALL of the real world flying skills). So, if you're sim only, and you'e positive it's going to remain that way for life, then don't feel obliged to be a hand-flying, raw-data compatible pilot unless you're motivated to do so.