How do ancestry websites work? Is it even possible to link back generations like that?

[wendy c]

"link generations back".
Of course. That is exactly what genealogy is...the use of records/ documents, which validate the relationship of persons, generally parent/child but also siblings.
Ancestry websites are not necessarily genealogy...all they are places for posted family "trees" (which frequently have errors), OR original records. A death certificate is one type of original record (even if it can have errors)..same for census records. Tombstones are a "record".
Ancestry sites DO NOT do the "work". You do. There is a key to it, which is the method. Starting with yourself, you PROVE your parents by a record. This makes a foundation to build with. Next, PROVE who each of your grandparents were, not by linking to you..but link your parent to them. Next..prove the parents of your 4 grandparents, using documents. You are not specifically named as their gr grandchild..the linking of the other documents creates the chain. You just keep going, by learning what the different sources of info are.
Genealogy has been around since before computers. I used to personally go to a courthouse, to find a will (those name children and wives). The process is about the records... the computer and internet is just one means of making records acessible. Persons who simply copy other family trees fail to know the WAY to use documents to insure having the right person/record..thus, passing along faulty information. If persons do good research, the trees can be good.
You just have to know the difference between the research process and how the computer can make it easier.