Actually, reading the original question I was not certain whether the poster was asking about the red rectangles during image review, or asking about them in the viewfinder.
In image review it's simply a matter of turning them on or off in the menu (I have them turned on in my camera, to help when I'm checking focus accuracy in images).
"Add image verification data" has nothing to do with displaying the focus points or not, either in review or in the viewfinder. Image verification is only used with supplementary software (sold separately), to determine whether or not an image is "as shot" or if it's been "Photoshopped". This is used by police, crime scene investigators and similar, when digital photos are being used as evidence and legal proof.
If we're talking about the red rectangles when the AF points light up in the viewfinder, we really don't have enough info yet. What those indicate differs depending upon the AF mode being used: One Shot, AI Focus, or AI Servo. It also differs depending upon whether you have the camera set to Single Point/Manual, or if you have All Points/Auto enabled, allowing the camera to select the point of focus for you. (Note: 60D only has those two focus patterns to choose. Other models have additional patterns. For example, 70D adds two more with Zone Focus and Expansion Points. 7D has a total of five: All Points/Auto, Single Point/Manual, Zone Focus, Expansion Points and Spot Focus. 5D and 5D Mark II have only the two - All Points/Auto and Single Point/Manual.... but has a limited Expansion mode that, when enabled, only works in AI Servo.)
One Shot is used for stationary subjects, flashes an AF point when AF starts, then flashes one or more again to indicate which have locked onto the target, at the same time that Focus Confirmation is given by the green LED lighting up and, if it's enabled, the audible "beep". In One Shot mode, you need to release the button and reapply, to make the system refocus.
AI Servo is used with moving subjects (also useful with varifocal zooms, if you zoom after focusing). The red rectangle AF point in the viewfinder lights up when focus starts and on 60D stays lit so long as the shutter release is kept half pressed. Focus never locks, it continues to be updated as the subject (or the photographer, or both, and/or the focal length of a varifocal zoom) move and the focusing distance changes, so there is no Focus Confirmation in AI Servo.
There's a lot more to the AF system and it pays to know it and how to control it. So I'd highly recommend the original poster view this half hour video on YouTube -
http://www.youtube.com/watch?v=iAx86nblZ2g - along with the two vids others in the series. These three vids are a seminar about Canon focus systems by Rudy Winston recorded a few years ago, recorded and posted on YouTube by B&H Photo in NYC. The 60D is newer and not included, but the 50D is discussed and it's AF system is identical to the 60D's. Some other Canon model AF systems are covered, too, that won't apply to 60D, but might be handy to know about.
If shooting action, the poster might also be interested in Back Button Focusing. This is a very popular technique among sports photographers in particular (though it's usable with nearly any type of photography). Here's an article aobut it written by Rudy....
http://www.learn.usa.canon.com/resources/articles/2011/backbutton_af_article.shtmlI heartily second the suggestion to buy one of the guide books for 60D. There are quite a few and they aren't expensive. I don't have a 60D, but have made a point of buying a guide for ever Canon model I've ever used, just to get up to speed and make best use of it as quickly and with as little fuss as possible. The guide books complement the user manuals nicely...
http://www.amazon.com/s/ref=nb_sb_noss_2?url=search-alias%3Daps&field-keywords=zeikos%20UV#/ref=nb_sb_noss?url=search-alias%3Daps&field-keywords=canon+60D+in+books&rh=i%3Aaps%2Ck%3Acanon+60D+in+books I'm sure most of the available guides are helpful. Just from personal experience, I can recommend those by Michael Guncheon, Charlotte Lowrie, and David Busch.
I have no idea your experience level, but if you're new to using DLSRs and photography in general, supplement the guide book and user manual with Bryan Peterson's "Understanding Exposure".
http://www.amazon.com/Understanding-Exposure-3rd-Photographs-Camera/dp/0817439390/ref=sr_1_1?s=books&ie=UTF8&qid=1396202163&sr=1-1&keywords=understanding+exposure Sometimes I think this book should be required reading for folks before they're allowed to post questions on forums!