It's not possible (at least not that I know) to specify Filevault's target dir. It will work by automatically working with your home folder by creating (if you are in Leopard or above) a Sparse Bundle (or a Sparse Disk Image if you are in Tiger). The reason for the change has to do with Time Machine (and to allow -to a certain extent- to backup a FileVaulted home).
However, you can pretty much "replicate" the functionality of FileVault for a specific folder(s) by using Disk Utility to create an encrypted sparsebundle image of the Folder in question. You'd have to mount this image every time you want to use it but the "effect" is similar.
You can create symbolic links to the files and add the image to the login items if you have an application that needs the data in its original location (which is pretty common). You will possibly have to add the image password to the "Keychain" for it to be automatically expanded.
It would be important to read about Time Machine's limitations too, since a FileVault home directory can only occur when you're logging in (or out). In order to make Time Machine to act as a regular, you need OS X Server edition as a target.
According to the wikipedia entry (which I should have quoted at the beginning since it has all this information, better written and more complete):
FileVault is limited to encrypting home directories only in versions of Mac OS X prior to 10.7, and only those directories in their entirety. FileVault can encrypt entire disks starting with Mac OS X version 10.7
(emphasis added by me)
It remains to be seen whether this is true or not, since we don't speculate about future versions, but keep that in mind.
As an alternative, there are "multiple" programs that will also help you keep a secure "vault" of things. I'm mentioning Exces because I got it from a Bundle a couple of years ago. I used it three times and it works; there might be free alternatives (as well as using the plain "Disk Utility").
Update: Added the link provided by Kyle, because it explains how to do it, but kept my answer because it's "longer" :)
OS X Internet Recovery
Mac models introduced after public availability of OS X Lion include the ability to start up directly from an Internet-based version of the OS X Recovery system. OS X automatically uses this feature when the Recovery System on the hard disk isn't available (such as when your hard disk encounters an issue, or when your hard disk has been replaced or erased).
My setup is a Mac mini 2011 with a DIY Fusion drive (840 Pro + 1 TB Hitachi). The Fusion drive was built on 10.8 and then the machine was upgraded to 10.9.
diskutil list
/dev/disk0
#: TYPE NAME SIZE IDENTIFIER
0: GUID_partition_scheme *256.1 GB disk0
1: EFI EFI 209.7 MB disk0s1
2: Apple_CoreStorage 255.7 GB disk0s2
3: Apple_Boot Boot OS X 134.2 MB disk0s3
/dev/disk1
#: TYPE NAME SIZE IDENTIFIER
0: GUID_partition_scheme *1.0 TB disk1
1: EFI EFI 209.7 MB disk1s1
2: Apple_CoreStorage 934.5 GB disk1s2
3: Apple_Boot Boot OS X 650.0 MB disk1s3
4: Microsoft Basic Data BOOTCAMP 64.9 GB disk1s4
/dev/disk2
#: TYPE NAME SIZE IDENTIFIER
0: Apple_HFS Fusion HD *1.2 TB disk2
When I press alt, I get three entries, Fusion, Fusion, Boot Camp. Either Fusion being selected boots the main OS. Bootcamp boots Windows.
⌘R boots local Recovery HD (not Internet Recovery). I have a choice of Wi-Fi, if I need Internet Recovery.
In your case, is it possible the Recovery HD is damaged?
Best Answer
If the Mac in question is running OS X 10.8.x or later, you can remove users from the list of FileVault enabled accounts using the fdesetup remove command. To remove the account using the username, run the following command:
Successful removal of the account will not produce any additional output.
If the account being removed is not currently enabled for use with FileVault 2, an error message will be displayed.
Does the icon you're seeing look like this?
If it does, this isn't a user account. It's a password directly associated with the disk's encryption. You will need to decrypt in order to get rid of it.