[smachiz]

That form also requires your SSN (or equivalent ITIN for non-citizens).

Using your passport doesn't obviate the requirement that they have your SSN or ITIN for the IRS.

The SSN card proves your eligibility to work, they still need to verify your ID separately (DL, voter card, etc.). They need both pieces. A passport counts as both.

[bitcoinmoney]

They need your SSN. Not specifically your SSN card. Source: lost my SSN card ages ago.

[smachiz]

Correct, if you have a passport or other eligible documents that attest your right to work. Your SSN card counts as one of the eligible forms of attesting your right to work but not your ID.

Which is I think what I said. They still need your SSN, just not the card itself.