Indeed looks like it mounts it as read-only or so that your user doesn't have write permissions..which in turn is probably caused by the method you use to mount your PSP. I didn't have a single problem (other than encoding videos to PSP-suitable format), but that was probably because I used the thing on Ubuntu, where udev set the permissions correctly when it mounted PSP automatically after I plugged it in (and selected "USB connection" from the device). If you're mounting it using 'mount' or trough an entry in fstab, it's quite possible that you don't get write permissions for regular users.
Actually what you mount is the memory card in PSP, so basically you could use any card reader and it wouldn't make a difference. The card has fat filesystem (known as 'vfat' under Linux) like memory cards usually have, so in that case I don't think it's sufficient to just run chown/chmod on the mounted directory; the permission settings need to be set in mount options, because fat filesystem doesn't know about user/group permissions like, say, ext3 filesystem would.
So if you continue having trouble, tell more precisely how you are mounting the device and if you have tried any options (try 'umask' if you're using the "manual" fstab/mount way for this). And add into your profile information the operating system you're using, it might help answering some questions more specifically.