I think you hit the nail on the head when you say it is a personal opinion, everyone has their own idea of what true regret really is.
From my perspective a regret is not really over a "mistake" you made or something you "failed" at - If they are a regret, this would be the idea of you that you realize you screwed up and moved on.
What I consider a real regret is when you made a decision that no matter what you do you just can not comes to terms with it or there is "get over it" path to be had.
It is something that every time you do think back on life, its one of those big ass red flags that nearly brings tears to your eyes - its a decision that makes you depressed and you know you just missed the train of your life...or...you really fucked up bad.
With that being said, can you live a life without any regrets? I would say it is possible as it is only a regret until you can surpass, once passed you can clear it off the slate, but realizing there things that can never be cleared, nothing you can do will change what you did and you know that it is to remain with your for life.
just my 2 cents.