Does SQL Server place shared locks on scanned records when using REPEATABLE READ
What if some other transaction updates a record so that it would match with my WHERE clause in the UPDATE statement, thereby violating the REPEATABLE READ.


That would be SERIALIZABLE READ, not REPEATABLE. REPEATABLE only guarantees that the rows that qualified for the WHERE clause the first time will not disappear or be modified. It doesn't say anything about other rows qualifying in a second read.