Right. He is wrong (unless you state in the contract specifically that they have ownership, in which case he is right). Do you have your own publishing company set-up? If you don't, and you're going to be doing this, you should. There are a lot of rights involved in the music business-- the song rights themselves (publishing), the master recording rights (the copyright to any particular recorded version), grand rights (usage in theater productions), and sync licensing (film and television), and royalty rights (for producers or artists that record for a label, but aren't the writers or publishers, for instance). Plus Internet sales and plays, which have kind of become their own thing. The publishing rights usually are administered by a publisher (publishing company), but artist-owned companies are set-up for that purpose as well. There are two different income streams that come from publishing-- the publisher's share, and the writer's share (which is split between any co-writers). If you are the writer, and also the publisher, you get both. You have to be affiliated with a performing rights organization (they take a cut for collecting payments) if you want to get paid for radio and TV airplay. The major organizations are ASCAP, BMI, and SESAC.
That's about all I feel like typing right now, bruh. This is a deep subject and you should learn your business. A lot of what's done in hip-hop, as I said, is in complete contrast to the rest of the business, because the practice of artists and labels and executive producers buying tracks outright became the norm long ago. It is still the norm, only for much, much less money than it used to be. Or, people get into the "beat leasing" thing which is not my area of expertise. But, you really need to get some good books on standard music industry practices. One that is very popular and pretty comprehensive is Donald Passman's book. Another was by the late-great producer Kashif. There are also a bunch of guides on publishing, and there used to be a book that came out annually called "The Song Writer's Market;" not sure what's happened with that in the digital age. But do your reading and your due diligence. Seek the counsel of a competent music/intellectual property attorney. It's good to know what you're talking about, even if you only make a couple of hundred bucks. If you "sell" that song, and it becomes a hit in 20 years, you're going to wish you had paid attention, and/or you'll want to know how to (attempt) to access some $$...
GJ