Just belonging to the same group (which I'm going to be generous and assume isn't wheel, because that would be bad) isn't sufficient.
For instance, if the files created by the web server have permissions set to "600", the ftp-user being in the right group isn't going to help, as the group doesn't have rights to read the file.
Even if the perms are sufficient to allow the group members to read the file, you also need to make sure that the right group is being set. If www-data's primary group is www-data, the file is going to initially be created with the group set to www-data. You'll need to make sure that it gets chrgrped to the shared group before the ftp user can read the files.
One way to accomplish this is to set group of the folder into which the web server is saving its files to the shared group. Files created inside the folder should then get their group set to the shared group, not to www-data's default group.