If one takes two frames with origin $O_1$ and $O_2$ and if a body $P$ is at rest, both according to $O_1$ as well as $O_2$. The body is at rest. If the frame is moving with a constant velocity, the same observation will not be made. Therefore a frame moving with a constant velocity cannot be taken as an inertial frame. Assertion is right.
But the reason given is wrong because the frame on which Newton's laws of motion are applicable is an inertial frame.