I don't think this is strictly correct. This implies that someone could start an atomic stopwatch at midnight on Jan 1, 1970, and it would match Unix time. It won't.
Because Unix time is non-linear and will either slew or repeat seconds when UTC has leap seconds, the hypothetical stopwatch would be ahead of Unix time by 34 seconds.
... at least this is how I understand it. Every time I try and wrap by head around the differences between UTC/TAI/UT1, my head really starts to hurt.