IRS site says I can electronically file my amended 2019 return that was rejected rather than mailing or faxing it in to IRS.

[DoninGA]

E-filing of a 2019 tax return closed after the end of October.  The amended tax return will have to be printed and mailed.

[Opus 17]

Not at this time.

First, "amended that was rejected" is a contradiction.  If your original return was rejected, you just need to re-file it as an original return.  An amended return that you mail can't be rejected.  So do you really only need to re-file your original return, or do you need to file an amended return?

Second, all IRS e-filing is closed until January 27. You could have e-filed an amended 2019 return using Turbotax (if your original return was also filed with Turbotax) up until October 15.  At this point all e-filing is closed.  We don't know if it will still be possible to e-file an amended 2019 return when 2020 e-filing opens on January 27.