Yes, broadly that understanding is correct.

In the Shwetambar Sthanakwasi tradition, the accepted original Agams are generally taken to be 32 Agam texts. The other texts that are found in the full Shwetambar Agam collection are usually regarded as later compositions or writings by acharyas and scholars, not as the direct, original shrut of Bhagwan Mahavir.

So, in simple words:

• 32 Agams are accepted as the main authentic Agams.
• The remaining texts are not generally accepted as original Agams by Sthanakwasi.
• Because of this, Sthanakwasi do not give the same scriptural authority to those extra texts as they do to the 32 Agams.

Important note

This view is different from some other Shwetambar traditions, especially the Murtipujak tradition, which accepts a larger Agam collection.

In short

So yes, your statement is basically right: Sthanakwasi accept 32 original Agams and do not accept the rest as original Agams.

If you want, I can also give you the list of those 32 Agams in a clean, easy format.