No, your interpretation is not quite correct. You do indeed use your own clock to determine the time of events in your own frame of reference. But you still need to account for the light travel time of the event. This is why you need both the position and the time of the event in order to do a Lorentz transformation.
To see this another way, suppose you saw two events at the same time, one two light-years away, and the other one light-year away. In your interpretation you would call those events simultaneous. Simultaneous events cannot affect each other in any reference frame. But if the two events were in a line, the light from the first event could have triggered the second.
To see this another way, suppose you saw two events at the same time, one two light-years away, and the other one light-year away. In your interpretation you would call those events simultaneous. Simultaneous events cannot affect each other in any reference frame. But if the two events were in a line, the light from the first event could have triggered the second.