That statement is not correct.
Standby Redo Log must be archived before the redo data can be applied to the standby database.
That statement is not correct either. While Standby can use a process which is like generating archive, archive is really being transported from the Primary database.
If we put our standby database in noarchivelog mode, then standby database does not generate any archive. Because of this Redo data wont apply to the standby database. Right?
Yes. If you switch modes the standby becomes the primary and needs to be in archivelog mode.
Is this the reason why we put standby database in archivelog mode?