You can attempt to have the data recovery service perform another recovery procedure on the external hard drive. The company may charge you for an additional fee(s) for the re-recovery procedure. You can explain your story and they may offer a warranty or discounted service considering your situation.
While you did perform a drive format using Disk Utility, you merely wiped what is the equivalent of a table of contents for the drive. So the files are probably still there, but the table of contents will tell the computer the drive is empty. It is recommended that you do not attempt to place/write any files on that drive until you can perform a proper recovery, either through software you're purchased or sent the drive in for recovery.
Regarding the availability of 465 of the 500GB drive. Manufacturers publish any drive made with user friendly capacity specifications. Even though you purchased a drive label as 500GB, the does does not, as a matter of fact, have a capacity of 500GB. You can read more about this here...
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http://www.tomshardware.com/forum/271049-32-500gb-hard-drive-shows-space-comp#6003769
About read-only files. Mac OS X sets file permissions based on the system user structure. More than likely, the data recovery company formatted the replacement drive on a computer in their office. Their computer has users & permissions just like yours. However, the only permissions that were set on the replacement drive were likely only the users on the data recovery company's system. When you received the drive, you were not set in the permission hierarchy as a user authorized to remove, write and/or copy the files contained within that drive. Note this is only speculation on my assumptions.
Things of this sort can be avoided completely by having some matter of backup service in your home or in the cloud. This LifeHacker article discusses the whys and how-tos of backing up your computer(s). Off-site cloud-based backup service CrashPlan is super easy and cheap. It will provide a backup solution for your computer and the external hard drive.
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http://lifehacker.com/theres-no-excuse-for-not-backing-up-your-computer-do-1547987206