How long an employer must keep your records?

Few days ago, I have contacted few previous employers for reference letters; I needed them as a record of my whereabouts for the last 10 years.

One employer said “they don’t have any records of my employment with them and wanted me to send them pay-stubs as to show my employment period with them and any benefits that I may have received.” I found that to be really odd and I felt strongly against sending them anything.

I was under the impression that companies must keep records of their employees for a period of 10 years or so.

I am not sure what the labor law in the US says about this, but any feedback on this matter would be appreciated.

Thanks