The club's medical team wouldn't be the ones to decide whether Saliba needs surgery.
Saliba would've consulted with/been referred to top private orthopaedic and neurosurgeons. Club doctors are usually physios and consultants, not experienced surgeons so do not decide who should and should not go under the knife. Unless he has an unstable fracture or a trapped nerve (which is arguably the worst kind of back injury for a sportsman since the operation is particularly long and nasty), doing back surgery on - by the sounds of it - a compression fracture is unnecessary and risky.
The fact Saliba will not even need bone cement injected is a good sign. A brace + pain meds is all he needs.
