If living relatives are giving details of their current/immediate family then you have no reason to disbelieve.
The issue I believe most of us are concerned with is being able to doucment our research, that does not mean to produce a certificate for every birth, marriage or death, but to be able to validate our sources.
Knowing the names is one thing, being told they were born in 1828 is another step, finding the correct birth reference is yet another step, validating that Joe Bloggs from Yorkshire is indeed your direct ancestor on a given line is something, I at least, aim towards.
For each person doing research, they will have their own level that they want to achieve.
My personal aim is to be as documented as possible (depending on availability and funding) on my 4 (grandparents) lines. Once I feel I have achieved that for me the next step is to expand on the families of my ancestors siblings. This is only one way of looking at the research.
6 months ago if someone handed me a tree and said "here you go, here's your ancestors to xdate" I'd have been thrilled, now I'd be greatful but it would be merely a guide for me. If however I was handed a tree that had references (be that an index ref, or a parish and date, or census ref) I'd be greatful and I'd want to see each reference for myself before commiting it to my tree.
I struck lucky in two ways, my paternal line has been pretty easy to trace (I've 12 generations and all within about a 25 mile radius) and my paternal grandfather's brother researched the same line 20 or so years ago. I don't have his research, just the tree he wrote (beautifully so), but it did give me names and dates. I trust his research implicitly because I know it was done with accuracy and no costs barred. I've built on that and using his dates/places/names I have been able to pull up index references that match and order some of those certificates.
As I've been going through my tree recently some of my own work has come back to bite me. I've looked at a person and thought to myself "now, how did I get that date for their marriage? How did I know that? Where did I get that info?" and I've simply had to go back and do that bit of work again to make sure I was right and this time noting the sources/references. If I can't remember where I got some info from, I can't know if it is right or not, with the source I can check I didn't make a typo or something.
Don't be offended that people want to verify sources and wouldn't just accept details from another tree, it's just what has been learned (often the hard way).
Do what makes you happy, otherwise it's a chore instead of a hobby =)