or that they did, in fact, emigrate before 1841 even though you cannot find the data
One of my ancestors emigrated to Australia in 1839/1840 (left England in 1839 and arrived in 1840), and thus does not appear in any UK censuses. However, there are plenty of trees which have added various census entries for him - there is a similarly named individual who has a wife with the same name, and people seem to ignore the fact that he (my ancestor) was born in Portsea in Hampshire, not Telscombe in Sussex (birthplace of those census documents). A lot of them also add a bunch of children also born in Sussex to their trees, which is strange to view when you take a look.
As for Public v Private trees on Ancestry, I have both. I have a single large unwieldy Ancestry tree which is public and includes every member of my extended family whom I have so far found, which has helped me find records I hadn't considered, find birth and death records that no other "public" tree has managed to find and allows those with DNA matches to attempt to judge their relationship with me. (There are plenty of people on that tree with unknown names - both first & last, and missing birth/death dates). There are most likely errors in that Public tree. I don't shy away from it, and deleted a bunch of people from a spurious marriage earlier this week - I had someone with two wives when in reality there were two different individuals with the same name. A lovely member of the wider Ancestry family (and always a possible cousin of mine, relationship at this point unknown) pointed out the mistake and I happily edited it (and had a long email conversation while it was happening and managed to help her add some information to her tree at the same time.)
I also have a bunch of private trees which I share with my wider family. Most of these are much smaller and have (hopefully) much fewer errors. Most of those are unsearchable, because most of the time any information I have found is already in the large Public tree anyway!
Two points-
One for public trees - I have so far found more cousins through Ancestry than I have through Lost Cousins (no harm to LC, I think it's a brilliant idea, but I am still only 1 cousin from it, with a bunch of relatives by marriage). One of my cousins I found because they were sharing a multitude of photos that had belonged to their grandparent - and my great-grandmother's family was incorrect on their tree. One I found because I'd accidentally added an incorrect photo somewhere, and they recognised the people. The last two, I found through DNA matches and their public trees. I think I have discovered almost 10 various cousins across Ancestry and DNA links from both sides of my family - Australian, British and Canadian cousins through my father's side, and a bunch of 3rd cousins in Canada, Australia and the UK on my mother's. I once had a conversation with a cousin who had sent me a message because I added a photo from his tree to mine and he wanted to know the connection.
One for Ancestry's Hints - I have also found the multiple hints for the same event across different record sets trying, but it has come to my attention that often those different record sets often have different information - for example I have had 2-3 records pop up for the same marriage, and while 2 will share just the year, 1 will have the actual date. It is similar for some baptism records. Often some of the cemetery records (particularly those from the US for some reason) also include information about parents, spouses and children that you might not have had previously.
And even thought some of the hints have been spurious (see above example of my emigrating ancestor whose Ancestry profile keeps randomly adding census hints), the majority that Ancestry offer are correct. Occasionally above and beyond information that I already have - sometimes they offer a correct census record with a married name before you've found the marriage index, etc. Frequently Ancestry will also generate new hints for ancestors you have already "cleared" the hints for - either by adding or ignoring, and it may not have been something that you have previously found.
But in the end, I have learnt a lot through trial and error when it comes to Ancestry hints. Occasionally when I get back to that leaf of my tree, I prune, remove and correct information I may have incorrectly added previously. And the unfortunate thing is, a lot of people do not get onto Ancestry knowing how to judge good hints/good records/good trees from bad ones. They have to learn and removing all information from them in the way of private or unsearchable trees is not going to help. (My profession is leaking through here).
I look at it simply. My tree is correct as I can make it, and I prefer that there is something correct on offer as a point of comparison if nothing else.