Do You Ever Ignore Misbehavior?

Do you separate the kids who are causing problems or do you put them all together? Here is a story from a former middle school colleague of mine (she wishes to remain anonymous)... 
"I did the one thing that you are always told not to do - I put the six students causing the most disturbances at a table together. I began completely ignoring all of their minor behavior issues. Of course, I wouldn’t have ignored any major offenses, but these were things like speaking out of turn, making noises, tapping pencils, getting up out of their seats without permission, etc. Things that, alone, do not seem like major problems until you have 6 students doing them on a constant basis.
I strategically placed them at a table beside the trash can and pencil sharpener. This way, when they got up out of their seat without permission, they didn’t have far to walk. The funny thing was, once the students stopped receiving attention for the negative behaviors, they began exhibiting positive behaviors to try to get my attention. They began raising their hands to participate in class discussions (something they had not previously been doing.) They began asking permission to get up out of their seats.
When I moved them, one of the boys said, “Why did you put all us bad people together???? This isn’t gonna work.”
I just said “I don’t know what you mean, this is just the way the new seating chart worked out.” 
Once the behaviors started I just continued class in a positive manner without even acknowledging them. They were all astounded. One started tapping his pencil loudly while looking at me and waiting on me to correct him. One boy got up, stomped purposefully over to the trash can, and stared up at me expecting me to say something. They also tried talking out of turn rather loudly. 
Every time, I failed to acknowledge it and they were completely flabbergasted. Their expressions were priceless. I just continued to ignore the negative behavior and instead praised other students for their positive behaviors. For instance, when another student raised his hand and followed the proper procedure, I would say, “John, thank you so much for how you always raise your hand before you get out of your seat.”
After only a couple of days, one of the boys started raising his hand. I praised him for his positive behavior and welcomed him into the class discussions. The other students at the table quickly followed suit.I had tried the typical behavior interventions including staying after class to discuss the issues, calling home/emailing parents, and office referrals. I had attempted to relocate the students away from distractions. I had tried a reward system. Nothing was working. Once I saw success from the alternate seating arrangement I was able to continue the positive behaviors by reintegrating a reward system with those particular students."
"The teacher's attention is the most powerful reinforcer in the classroom," Fred Jones