The problem with this statement is that it is simply factually untrue, and it represents a fundamental misunderstanding of what constitutes information.
Information is measured in bits and bytes. Ones and zeros. Or, in genetic terms, As, Cs, Gs and Ts.
Information in the genetic code can be changed through mutation. Mutations come in several forms, such as insertion, deletion, substitution, duplication and so on. These have all been observed happening in the laboratory.
Insertion and duplication, by definition, add new information for starters.
People who think that information can’t be added to the genetic code also tend to think that “password”, “qwerty”, “123456” and their date of birth are strong passwords. And then they wonder why their Facebook account gets hacked by someone in Tauri-Hessia.