I suppose the safest way to live a life is trust no one, rely on no one, believe no one and just go it alone. Is it possible?

Nope.  Human beings are inherently trusting.  They WANT trust.  Unfortunately, most humans are selfish (meaning they care more about themselves than others).  When push comes to shove, it's "me first" - and they'll lie, cheat and steal to make sure that happens.  Therefore, people learn quickly that they can't trust everyone, nor can they believe everything others tell them.  Yet no one can "go it alone" (despite what many may claim or think).  We NEED others.  If everyone trusted no one, believed no one, 90% would die within a year and the rest would become paranoid.  {No, things wouldn't be like what you see in the movies.}  If you can't truest anyone they must distrust them.  After all how would you know if what they do or are planning to do isn't to your detriment?  How do you know that they aren't plotting against you?  What if you were unable to find any food and someone told you where you could find some?  If you can't believe or trust them, would you go where they told you or would you go somewhere else... just to be safe? (maybe it's a trap?)
No, we MUST believe and trust others - even when some betray our trust or lie to us.  Not everyone is out to deceive you (that's paranoia).  However, we have enough intelligence to distrust those who break our trust (until they re-earn it) and not believe those who constantly lie to us.