The more accurate statement is that all objects have the same speed in spacetime. Time is just one dimension of spacetime and objects do not all travel along that dimension with the same speed. For example, an object travelling through space at close to the speed of light will have a speed along the time dimension close to zero.

Having said that... this is mostly a slogan and makes for good Youtube videos, but it falls apart the moment you subject it to even the most basic scrutiny. For one... it doesn't make sense to talk about a speed through time since speed is literally a measure of change with respect to time, so a change in time with respect to time doesn't make any sense.

But as a slogan, it captures the idea that motion through space and the rate of your own clock are tightly linked together.