[Nyororin]

I am going to agree with your friend that there are only three - unless you must consider arabic numerals themselves as a separate writing system.

The reasoning being literature. Even in the silliest light novel, you are not going to encounter anything written in romaji. At least, nothing Japanese. If used, it`s going to be for a foreign language or given name.

When things outside of advertisements and cute little not-really-meant-to-be-read slogans on products are written in romaji - THEN it might be considered a fourth writing system. Until then, it`s still really just a novelty.