It is true...to a point. The VA offers something called the Educational Assistance Allowance for trainees under the Survivors' and Dependents' Educational Assistance Program (DEA), which is lengthy title that basically says this:
DEA provides education and training opportunities to eligible dependents of veterans who are permanently and totally disabled due to a service-related condition, or who died while on active duty or as a result of a service related condition. The program offers up to 45 months of education benefits. These benefits may be used for degree and certificate programs, apprenticeship, and on-the-job training. If you are a spouse, you may take a correspondence course. Remedial, deficiency, and refresher courses may be approved under certain circumstances.
Full-time students can receive up to $915.00 per month for 45 months while they are in school (according to the VA website). There are smaller payment plans for those not going full time. My cousins both attended Texas Tech tuition free (their father was killed in a training accident just after Vietnam).
So, college isn't necessarily all paid for (depending on where they go), but a large chunk would be. All the info is at the VA website under the Education tab.