There is some truth in much of this. I do computer forensics professionally so this is very authoritive information from the horses mouth.
If there is a "determined", no cost effort to recover data then your probably out of luck, they'll get it back even if it's been wiped or overwritten by new data. The techniques to do this are called reading "border" and "shadow" data. You can look it up if your interested but take it as written, by someone who's watched it done, it's only a matter of money. It's even possible to recover multiple data streams from the same physical locations, not reliably, but it can and has been done.
Fortunately, few will be willing to fork over the many thousands needed except for maybe the government, so a standard, 3 pass wipe of deleted data is pretty much adequate to the job. This doesn't say that there aren't plenty of references to illicit data elsewhere on the disk, such as the explorer index file, the page and hibernate files. All these are gold mines for the forensics investigator, but a 3 pass wipe will stymie all but the most determined (as in "expensive") attempts to recover deleted data.
If you run a wipe program on a disk, either once or as a real time, background task that overwrites deleted data, the investigator will know you did it, and in many cases, that's considered incriminating evidence in itself and will be used by the prosecution if it's related to a crime.
If you want to safe wipe a disk, a format, high or low level won't do it. I don't care how you format, all that does is rewrite the sector and cluster marks, it doesn't touch the data. I can still get everything off the disk just as easily as if it were never formatted at all. Pictures, text, even programs or complete desktops. There are tools for that job that cost thousands of dollars, but their real pro at what they do. Give them a disk and they'll suck it dry. Safe wiping requires running a DOS based, forensics quality program that rewrites data a full seven times to eliminate shadows and borders on the data bits.
A seven pass, forensics wipe is pretty much proof against any recovery effort. Maybe the NSA, or the CIA might try it if it were important enough, but in my experience, they'll get next to nothing.
In our office where I'm the systems admin, no hard disk leaves the house intact. We dismantle them for decorations or simply destroy then in a press. It's just easier that way.
There is a whole cadre of hackers and scammers who do nothing else these days but go to flea markets and garage sales to buy up old computers for a few bucks each, I don't guess I need tell you why.
Al