Of course. Conspiracies have been confirmed to happen and I would also say that conspiracies exist that we don't know about.
So, to think like that. It makes you a conspiracy theorist. You may not be totally sceptical about too much but you know we aren't told the truth in some or even many cases, whatever the scenario, right?
Of course, we can argue percentages of how many percent of official lines does it take a person to question for them to be labelled a total crank or mentally unstable, against someone who maybe sees some stuff that needs questioning, who is termed rational enough to do that.
The point is, one persons inquisitive mind may surpass another persons, where trust is concerned. You know, you can get one person who delves deeper whilst another person will simply accept that one or two things seem dodgy, yet no need to go into detail about any other stuff.
If we can be lied to, we can be LIED to on many many issues. Finding out the real full on lies with many things is beyond most people's capabilities, physically and I'm sure you know this.
Mentally, they have many questions. Those questions can be answered by asking anyone who believes the stories that are told. The problem is, it's only a regurgitation of the info that is being questioned in the first place, told by those who bought into the info through basic third party chit chat/reading, etc.
If a stranger walked up to you and said, " your neighbour is a burglar and sells drugs" and you and your other neighbours all saw him/her as a model citizen or a pillar of society, helpful and courteous, who was giving, etc, etc, etc...you know the drill. Your reaction would be to either politely bid the gossip monger farewell or call that gossip a crank or trouble.
You may tell all your neighbours what you were told. Even telling the one accused, yet you would not think for one minute about questioning the accused, right?
Imagine 10 years down the line, you find that what the person said was absolutely true. You'd be in shock, right?
Now I'm not saying you have a neighbour like that but you know what I'm talking about. I bet you have witnessed the scenario I'm giving out, as well as many on this site will have.
Hidden in plain sight and plausible enough to carry it off.
A conspiracy about the earths shape though? A space travel conspiracy?
I don't think so. These things can be verified independently in more ways than any sophisticated conspiracy can account for.
Seriously, what can be verified? Forget about old books and what was told from times past. What can be independently verified without having the info given to you?
All you can do, is base what you know on the trust of what you are told about how things work.
If you can personally verify stuff, physically then what can you verify?