This (and all the other "helpful" search supplements) should definitely be under admin control. However, there is a fairly dependable work around for it which we use for students, and that is by having student searches use google's "simple" search url. Here are the instructions I've posted previously:
You do this by changing the setting "Omnibox Search Provider Name," under Devices > Settings. Set the dropdown arrow to the lock option, put Google (or whatever you'd like) in first two boxes, and then set the search URL to:
{google:baseURL}search?q={searchTerms}&udm=14&{google:RLZ}{google:originalQueryForSuggestion}{google:assistedQueryStats}{google:searchFieldtrialParameter}{google:searchClient}{google:sourceId}ie={inputEncoding}
Hope that helps!
