Some external influence is locking the files. Could be anything from virus scanners to Windows' own thumbnail/ preview mechanisms, in particular if you use Windows pre-defined "folder types" for media, music, documents, photos etc. instead of just defining your folder as a generic file folder or storing your files outside the default user folders...
I don't have anything in a pre-defined folder... (Like the "My Music" or "My Documents" folders.) Everything's in its own system of files on my hard drive. I'll try messing with my anti-virus program and see if that changes anything. Thanks!
Found the problem - in case anyone else has had the same issue! AVIs and FLAs were in the same folder together. For some reason that confused AfterEffects. I tried moving the AVIs into another folder by themselves and AE imported them all at once, no problem. Hooray!