cron apparently requires a newline character on its own line at the end of the file

Is this a bug?

No. I created a file with no newline character at the end. Nevertheless Vim (after :set list) shows $ at the end. It looks like your premise is false, your file is missing a final newline, cron works as intended.

Notes:

• POSIX requires a trailing newline character to consider any line to be complete.

  3.195 Incomplete Line
  A sequence of one or more non-<newline> characters at the end of the file.

  […]

  3.206 Line
  A sequence of zero or more non-<newline> characters plus a terminating <newline> character.

  So the behavior of cron is not just an arbitrary quirk (although the tool might not be that restrictive). For more insight see Why should text files end with a newline?

• Vim with default settings will fix the missing newline while saving, unless you tell it not to.

• To tell whether there is a newline character at the end or not, make a hexdump of the file, e.g. hexdump the_file or xxd the_file. In case of your crontab this may be hard. In my Debian the crontab is /var/spool/cron/crontabs/kamil, but since I have no access to /var/spool/cron/crontabs/ as a normal user, I cannot just xxd the file. To overcome this I can use the following trick:

  EDITOR=xxd crontab -e
  

  There is a newline at the end iff the last byte reports as 0a.