The $17,000 threshold is for whether the GIVER of the gift has to file a gift tax return.  "Gift Tax" is somewhat of a misnomer.  Even though a gift tax return may be required, for individual  gifts over $17,000, very few people ever actually pay federal gift tax. The purpose of the gift tax return is usually only to document a reduction in the allowable estate tax exemption.
See https://turbotax.intuit.com/tax-tools/tax-tips/Tax-Planning-and-Checklists/The-Gift-Tax-Made-Simple/...