You're right to be concerned. It could be that the link file is not working to automatically point it to Adobe Reader to enable its opening. Providing you're sure the file is safe, save the file to where you can retrieve it.
Then open Adobe Reader and get it to look for the saved file by clicking on File/Open and locate the file.
If that doesn't work, you could right click the file and choose the programme to open it, ensuring that the box is ticked to always use Adobe Reader to open that type of file.
If that doesn't work, it may be advisable to uninstall Adobe Reader and do a complete reinstall. I believe Adobe Reader 9 is the latest version. Let us know how you get on.