According to the ownCloud documentation, if you enable encryption, file sizes can be ~35% larger than their unencrypted forms.

From my understanding of encryption, the file sizes should be more-or-less identical (perhaps some padded 0 bits at the end to make it a multiple of the key size).

Is that incorrect? If not, why?

Most likely, the encrypted file is base64 encoded which would account for 33.3% file increase (you encode three bytes of data in four bytes of base64 data).  Inserting a new line every 64 characters to make it easier to read (as is done by ASCII armor in openssl, GPG, PGP) will increase the size by 65/64.

Combining these two effects results in the new file being (4/3)*(65/64) = 135.4% of the size of the original or an increase in file size of 35.4%.

I've gone through the calculation in this answer here.

You are correct though that encryption should not need to significantly change the file size.  It possibly adds a couple blocks of data if there is a header, an initialization vector/nonce, some padding to make it a full block and/or MAC to check integrity, though these changes will be insignificant for large files (e.g., adding four blocks to an AES encoded file that is 1 MB would make the file 0.006% larger).  

However, to not increase the files size, you need to be fine with storing and passing around the encrypted data as an arbitrary binary.  Arbitrary binaries are often blocked over email to prevent spreading computer viruses, and are often difficult to open outside of hexeditors.  Base64 encoded files are easier to pass around and is a more portable format than binary files of an unknown file type.
