What possible alternative is there??? For a stationary observer, if the relative velocity between the ship and the light beam is c then the ship must not be moving. For a stationary observer if the ship is moving and the relative speed between the light and the ship is c the the speed of light is NOT c.
Say there is a space ship that has one headlight on the side of it. The ship is in motion and then the headlight sends a beam of light in a direction perpendicular to its direction of motion. The observer on the ship then measures the beam to travel a distance according to his own clock, d' = c t'. It then passes by a space station that then notices that the beam of light from the ship being sent perpendicular to its direction of motion travels at the speed of light, but then has a vector of the velocity of the ship. It travels at an angle, so that the beam moves forward in the direction of motion of the ship, and has a vector in this direction that is the same speed of the ship. It is then measured to travel at an angle according the stations clock that is at rest, d = c t. The ship is also measured to be traveling with a velocity according to the stations clock that is at rest, d = v t.
Then you have three distances, and then you can translate the distance the ship has moved down to the location where the beam of light has reached. This then forms a right triangle. You can then calculate the difference of the two clocks as they measure the single beam that is at the same location relative to both frames using the Pythagorean Theorem, $$ a^{2} + b^{2} = c^{2} $$
$$ ( v t )^{2} + ( c t' )^{2} = ( c t )^{2} $$
$$ c^{2}t'^{2} = (c^{2}t^{2} - v^{2}t^{2}) $$
$$ c^{2}t'^{2} = c^{2}t^{2} ( 1 - \frac{v^{2}}{c^{2}}) $$
$$ t'^{2} = t^{2}( 1 - \frac{v^{2}}{c^{2}}) $$
$$ t' = t sqrt{ 1 - \frac{v^{2}}{c^{2}} $$
So then the proper time, is the amount of time both observers would measure so that they both measure the same speed of light while they measure the same beam of light at the same location simultaneously.