As it says, 'phones stop that [trusting everything is ok] from happening. Instead of getting accustomed to being out of touch for a while, now we are always able to be in touch.'
But I think at the same time, we're all so aware of the fragility of life so much more. My parent's generation seemed to not care at all, trusting that bad things can't happen to us. My generation, I feel, are aware that they can, and do. So we try to optimise to avoid it, to mitigate it, reduce the attack vectors.
Is the world different now too? In the UK, you're never far from someone with a knife and an attitude problem. You know not to argue or protest, to intervene or become involved in anything, for fear of someone with a 'zombie' knife attacking you, and the problem is kids are more mixed, not yet sorted into their social bands as we adults are. So your nice to do child might be mixing with a zombie knife carrier which increases the probability that something could go horrible wrong.
And the above is just one example of how people are thinking ahead, but multiply this by several different potential areas of concern and yes, you have a parent that worries.
But was it better to have parents that didn't seem to care?