This is an error from his part. He used the wrong conjugation for the verb to be. In grammatical terms, the subject pronoun he said is they and the correct conjugation, in terms of to be, should be were.
The BBC cannot be depended on anymore for the use of impeccable grammar.
Here, however, the newsreader is correct: 'none' can take both a singular and plural verb, depending on the intended meaning:
When you are considering things as a collective group (the notion of a sub-group within a larger group), use the plural:
“She had many boyfriends and love affairs in her younger years, but none were very serious.”
“Many factors contribute to rampant disease in African countries, but fortunately, none of these are present in South Africa.”
When individuality is being emphasized (that is, ‘not a single one’), a singular form of the verb is used:
“She is difficult to describe physically - none of her features is particularly striking.”
(That is, of all her facial features, not one is striking.)
“It was a quiet night in the restaurant. There was an elderly couple in one of the booths, but none of the other tables was occupied.”
(That is, not one table, not a single other table was occupied.)
Oxford dictionary shows these two different meanings (singular AND plural use):
pronoun
• not any (plural): none of you want to work
• no person; no one (singular): none could match her looks.= not one person could match her looks.
The newsreader is saying that not ONE of the students WAS injured.