Ivory is also typically only used for the keys, and doesn't actually impact the tuning of the instrument.
They exist, but they are notoriously difficult to tune and keep in tune compared to iron framed pianos. I think they have stopped making them for quite a while. I find it hard to imagine a high school using an instrument requiring so much maintenance.
If it was indeed a wooden framed piano, it was probably more of an antique than a practical instrument, and so, maybe with ivory keys, though again I doubt it.
That also made them pretty finicky, changing moisture and temperature would have a significant effect on the pitch of the piano. At that time 'standard pitch' was about A4@423 Hz, considerably below what it is today (A4@440), which lessened the problems somewhat but if you wanted to have your instrument well tuned you had better learn how to tune it yourself.
For harpsichord players (the predecessor to the piano) today self tuning is still the standard.
Piano history is fascinating, if you are interested in the subject I'd recommend reading 'Of men, women and pianos' by Arthur Loesser. It's an old book but a fantastic source of historical information about the development of the piano/grand piano.