CS PhD Late Letters

Hi, most programs I'm applying to have a deadline of ~ December 15. I'm applying only to top US schools and one in Switzerland. One of my recommenders said that applications start being reviewed in the new year and are rarely seen in the holidays, so they'll send their recommendation by the first week of Jan.

​

I'm a bit anxious as I saw a few Quora posts that said if the application is incomplete (LoR missing), it isn't evaluated and you've basically lost your shot without even being evaluated. Could someone please help with any information from a valid source?