Background Checks: Employment Verification for Permanent Resident: I-9

My question involves labor and employment law for the state of: NY.

I chose background checks as it was the closest topic but technically it's not, as it happens after the employment.

I am a permanent resident and I'm a freelancer, therefore I fill out I9 every week as I work for different company based on projects and it goes through different payroll company. It almost always happens within first 3 days of my employment, not before the employment.

I give them My DL info and SS#, and I fill out front with my permanent resident card info.

I show them my DL and copy of my SS card when I'm asked.

Do I have to show my permanent resident card when they ask, even though I'm providing them with DL and SS card?

Link below says employer cannot ask for a specific document, such as passport or greencard, but I feel like I'm being asked more than not recently.
http://ift.tt/1VRW81G

Just wanted to hear some opinions.

I know it's a question right in between immigration law and labor law; please let me know if I should migrate to immigration law forum.

Thanks for all your input in advance.

Background Checks: Employment Verification for Permanent Resident: I-9