I love a good circular argument! I was writing my initial post in a word document to make sure I said what I wanted to say and didn't waffle, but alas school duties (my full time job!) has got in the way (it's the end of the year... so marking, marking and more marking... except when you're getting the 12s to do revision.)
So I will attempt a precis of what I was originally going to say.
I use both Private and Public trees, although my biggest tree (and I would hope I'm not just a name collector) is my Public one. I like to think that people can do what I did, and learn to sort the information that Ancestry provides in order to become a better researcher. I admit to have learnt that way - often pruning my tree to remove erroneous information - for example an incorrect marriage when I ordered the death entries for a couple of ancestors that revealed the married names of two of their daughters. I also recently pruned 50 odd people off my tree after an inquiry as to whether I was related to a particular set of people... the information wasn't credible enough, so I deleted everyone and pruned it back to what it was, and then replied to the person to state I wasn't sure. I am fully aware that just because the chance is there someone people will ignore it, after all I teach teenagers.
Often I find that some Ancestry trees can help to add siblings/children to a tree, but I prefer any additions to be matched to records and often they are. If they're too unbelievable - had a child born in South America in the middle of siblings born in Amsterdam, I simply remove them as incorrect.
There are a lot of credible public trees out there, and an equal amount of people who simply add whatever Ancestry offers. I disagree with those who think that Ancestry hints just offer dross - usually (depending of course on the amount of information added) the initial hints are usually correct, once past the initial set of hints, it gets more and more inaccurate, or duplicates information you already have from a different set of data.
I will concur with Bob about the messages, I think I receive more messages from people with public trees than I do from private - that's not to say that I don't receive messages from people with private trees - the first cousin I emailed through a DNA link had a private tree (and is also on LostCousins somewhere) and happily told me when and where we were related, but I don't have many conversations with that particular cousin - and there's no real sharing of resources (I am not complaining, simply stating fact), most definitely not the sorts that I have had with other members I have contacted.
At this point I have been gifted more contacts through Ancestry than LostCousins (although I'm sure that will change), and definitely more cousin links through Ancestry at this point in time, both with and without DNA. I admit to not always contacting people I have Ancestry links with, although sometimes I don't get an answer that contains enough information. But I am always happy to do what I can even for those who are not blood related - I have happily shared information with others who are both cousin and marriage links alike through what I have, although I don't think I necessarily have that much! I generally start my messages with a query about being a possible relative - stating where I think it is if I have an approximate idea myself, and I let it go from there - I have never asked for access to someone else's tree although I have been gifted access to a couple of other trees, one for the purpose of sharing research that I don't have, and the other to see if we can figure out where we are DNA related as currently there are no shared names or links.
As for DNA links - I agree, "no tree" is the most frustrating response, especially if they don't have any links with "shared matches" you can identify. I have access to DNA tests for both my parents and my paternal grandmother (as I have previously stated) and so there is an inordinate amount of matches to dig through - including some second cousin links.
I think I ended up waffling, but I responded!