How to double-check and not pester airport officials?

I was reading this article. In it the author says -

Not checking and double checking

A hard and fast rule I have learned over the years is to double check everything. Just because the gate agent said your connecting gate is B6 does not mean it has not changed. Just because an airline ticket agent says the flight is full and no room to standby, does not mean that other passengers might be late, opening up seats. Just because someone says you cannot get a free hotel room due to an overnight flight delay does not mean that said person was misinformed or unclear on the rules. Never pester and always be polite, but just because someone says something is so, does not always mean it is so. At airports, it seems people are more eager to tell you something to move you along rather than to genuinely be right. - aviationrepublic.com

Now here the author sort of contradicts himself saying that you should not pester and yet double-check things. How is a person supposed to double-check without appear obtrusive/pestering ?

Update - I was thinking about this -

Just because an airline ticket agent says the flight is full and no room to standby, does not mean that other passengers might be late, opening up seats. - aviationrepublic.com

Now either the author didn't think this one through or what is he trying to say here ? Is s/he talking about the scenario where you bought the tickets say a week or two ago and now you come to know that it's been overbooked and you hang around hoping to see someone cancelling and hence you get a seat on the plane or is s/he talking about something else entirely ?