I think one thing most people fail to realize about frequency is that it is a separate variable from volume. As an aside the 3 primary variables in program design being frequency, volume, and intensity as measured by % of your 1RM for a given lift (i.e. weight on the bar). Volume and intensity over a period or session combine to equal workload with calculated tonnage in core lifts being helpful to track in many cases. A good piece for some definitions is here:
http://www.qwa.org/articles/tmethod.asp
Anyway, frequency serves to distribute volume or workload over a period of time. Take a lifter who handles 10 sets of legs 1x per week. What most people do when they try to increase frequency is come in and do the same thing 2x per week. Now we have 20 sets per week or a 100% immediate increase in workload - likely not going to happen if things were setup even remotely close beforehand. Over time, this lifter might certainly be able to handle the increase but not 100% at once or even close to it. The correct way to use frequency is to distribute the original 10 sets i.e. perform 5 sets 2x per week. This works a lot better and frequency is really important to increasing weight on the bar and getting better at lifts. Actually this lifter will probably find very quickly that he can rachet up the workload much better with this distribution rather than doing it all on 1 day.
You don't get accustomed to a movement very well doing it once ever 7 days. You don't need to do it every day 2x per day (although in a more technique based lift like the snatch or clean higher frequency is very helpful) but 1x ever 7 days or more is pretty bad and the whole overtraining thing has a lot more to do with the CNS that muscular recovery and aggregate workload over a period is a better way to guage CNS impact than frequency in isolation as overtraining is systemic accumulated fatigue on the CNS (i.e. what is stimulative over 4 weeks might drop someone in their tracks if done for 8 weeks without rest).
To illustrate this better a lot of guys who use 5x5 style programs based on Starr's or Pendlay's stuff squat 3x per week. Even raw beginners, even elite lifters. How is this done, most people think the frequency is impossible. Well, you walk everyday many times without problems so frequency alone is not the issue. It's the combination of volume and intensity (or workload) over a period. Frequency merely distributes this workload. For a beginner, workload is low, and they will set new records possibly 2x per week. For an intermediate workload is increased and they might add weight to the bar weekly or thereabouts. For an advanced lifter workload will be higher still and new records set every 4-8 weeks.
Something like this:
Beginner: 3x5 performed 3x per week. 1 day is light. Weights are ramped to a top set i.e. 100, 115, 130. New records 2x per week on top set.
Intermediate: 5x5 performed 3x per week. Heavy/Light/Medium. Weights are ramped to a top set similar to first. New records set weekly on top set of 5.
Advanced: Periodized to allow for higher workload. 5x5 performed 3x per week. 2 Heavy and 1 Medium, Weights are constant set weight i.e. 315x5x5. This might be dropped to 2x per week with 1 heavy day and reps of 3x3 after the initial period (i.e. loading and deloading). New records every 4-8 weeks.
Thinking about tonnage in the core lifts as a proxy for workload. An intermediate and advanced lifter with exactly the same max lifts (rare) might have the intermediate using 30,000 lbs weekly or enough so that fatigue never really overtakes him and he can set new records weekly on a linear basis. The loading period for the advanced lifter might have 50,000 lbs per week - and he will likely fatigue from this in a few weeks and require a period of lower workload (volume lowered, frequency lowered, but intensity or weight on the bar can still be kept high - lots of ways to handle this but workload drops). Maybe workload is 20000lbs at this point. A frequent way people might do this is 3:1 ratio. So 50K loading and 20K deload in this example (which is pretty random by the way, don't go extrapolating all kinds of crap from it). What's the one thing you notice though, over 4 weeks you have 170K in workload (50K x 3 weeks + 20K x 1 week) vs. the linear 120K (30K x 4 weeks). Much higher average workload - how is this possible. Dual factor model or fitness/fatigue. Fitness and fatigue are separate and acrue and disipate at different rates. Fatigue can be disipated in 1/3rd the time of fitness i.e. you can handle a lot more work over a limited period (with a short period of rest) than you can running indefinitely without limit. This is why some people here might have gotten great results doing a ton of work over a few weeks and than as fatigue accrued it burned them out. If you want to better understand the dual factor model and how this is handled a good read is this:
http://www.higher-faster-sports.com/PlannedOvertraining.html
So anyway, this is probably way beyond what a lot of guys on here are doing. That said, this is pretty much how training is handled around the world in elite strength and athletics. There is more to training that picking some exercises, spreading them out in a 3 day split, training a lift 1x a week, and with no other thought or organization, going in, working hard, and hoping to get bigger or stronger for your efforts. This might work decently enough at the beginner level but optimality and organization plays a far bigger role further out and even for the beginner, getting this right will make a big, very noticable difference.
So - back to the original point. Anyone can handle whatever frequency they choose. It's a matter of workload over a period and the conditioning of the athelete. Anyone can squat 3x per week just as anyone can walk every day, you just can't do 10 sets of 10 to failure or some garbage like that or increase workload 300% instantly to try it. Same with walking every day, you can't do maximum sprints for hours every day and you can't take a couch potatoe and expect him to walk 15 miles without some issues.
I hope that helps illustrate some things as this is a pretty good thread and I imagine we are touching on stuff that most people on this board either never considered or never realized were part of training. Keep in mind, the most important thing is adding weight to the bar and getting your lifts up. Now, how to best go about that for a given lifter at a given point in time - now that's programing and training, suffice to say you want to make the fastest progression possible and workload is a factor in this process.