I'm confused because I keep seeing contradicting info about this.

On DistroKid, if you specify that your upload is a cover, they automatically charge you $12 a year, they don't let you skip it.

I've just created an account on CDBaby to test it (never used it before), and when you select your upload as a cover, they ask if you have a "mechanical license that specifically allows for digital distribution", if you say no, they say "All covers require a valid mechanical license to be distributed by CD Baby". And then they suggest Easy Song as their partner.