Copying a WordPress website and media files

I moved a website from one hosting company to another. I then realized the images in the WP Media Gallery were not showing up in the WP media gallery view. So I contacted the support staff at the hosting company. They told me that just moving them would not make them visible to WordPress. For them to be available via the media gallery they must each be reuploaded using the media upload function in wordpress.

Is this true?

Thank you,
Joe