The statement is true and describes one the most common use cases of mobile cloud service providers. Using a cloud service like iCloud or Google Drive ensures a lost, stolen or broken mobile device can have it's data recovered and transferred onto a replace device. Depending on the service and device configuration this could include Contacts, Apps, Emails, Pictures and nearly any other file type.
Cloud storage is a model of computer data storage in which the digital data is stored in logical pools, said to be on "the cloud". The physical storage spans multiple servers (sometimes in multiple locations), and the physical environment is typically owned and managed by a hosting company. These cloud storage providers are responsible for keeping the data available and accessible, and the physical environment secured, protected, and running. People and organizations buy or lease storage capacity from the providers to store user, organization, or application data.
Cloud storage services may be accessed through a colocated cloud computing service, a web service application programming interface (API) or by applications that use the API, such as cloud desktop storage, a cloud storage gateway or Web-based content management systems.