Between half and three-quarters of nursing home residents fall each year.That’s twice the rate of falls for older adults living in the community. Patients often fall more than once. The average is 2.6 falls per person per year (Center for Disease Control, CDC)
The answer to your question is, yes, it is true that the rate of falls amongst the elderly in nursing homes is higher than the rate of falls among the same age group living in the community. You can confirm by the CDC statistics quoted above. In addition, while 5 percent of the 65 and over population live in nursing homes, these nursing home residents make up 20 percent of the deaths from falls.
Prevention requires a multi-effort cooperation from all branches of nursing home medical care. It includes cooperation from "medical treatment, rehabilitation, and environmental changes." The CDC gives a very detailed analysis of preventive actions required.