No, it is not correct. The only thing that matters is the size of the image in pixels. As long as that is the same the quality, from the view point of resolution, is unchanged.
Dpi is used as a synonym for ppi, which is pixels per inch. Note the word "inch". Computer files don't have inches, only prints do. The dpi number is an arbitrary default size for a print to be made from that file, but even then it isn't really relevant because the
real ppi will be the actual number of pixels divided by the actual inches of the print.
In PS you can easily change the default number to anything you want, 300 or 3,000.