An object falling into a black hole appears to slow down as it approaches the event horizon, taking an infinite time to reach it.

This statement is TRUE from the perspective of a distant observer. Due to gravitational time dilation, light from the falling object is increasingly redshifted as it approaches the event horizon, making it appear to slow down and fade without ever actually crossing (infinite time). However, from the falling object's own perspective, it crosses the event horizon in finite proper time. The infinite time is only for external observers, not for the object itself.