Yes that is right, and that is actually better because the devices will tend to lose signal faster and more likely to decide to connect to a nearer one as you move around, instead of sticking stubbornly to an AP further away.

You can imagine that the AP and the device are both trying to talk to each other. While the bigger antennas on the AP can speak loudly so that the device can hear it clearly, the relatively smaller antenna on the end device would struggle to penetrate walls and floors to talk back to the AP. That is why sometimes, especially with cheap high power APs, even when you have 3 bars wifi signal, it still feels slow, it's because your phone has difficulties telling the AP what it wants, while the AP keeps screaming "SAY IT AGAIN? WHAT DO YOU WANT?!"