Well yes and no. It’s a ballistic missile, so it doesn't have a "low trajectory" but a ballistic flight path, which can be calculated from just 3 data points. It can indeed maneuver at all stages, but because it's really fast (that part isn't a lie), it's only able to do very small deviations from it's predetermined flight path (apart from also needing to hit the actual target, so it can't just fly in a completely different direction). The deviations are so small that the patriot can just correct for them in many/most cases. So it's not a lie it can maneuver, it's just not as much as would be necessary to reliably avoid interception, even though patriots fly slower.

As I see it, there are 2 flaws with your thinking: First, even a wildly manoeuvring missile eventually has to point the nose at the target and dive in. It is vulnerable then at the very least. Second, manoeuvring alone does not render something immune to interception. For example, fighter aircraft manoeuvre like crazy and they get shot down handily.