A satellite in LEO already has a speed of about 8 km/s. The highest speed of a satellite in a highly elliptical orbit is 11 km/s. It you can shoot a satellite at 8 km/s, you probably can also shoot it at 11 km/s.
The problem is, of course, that the perigee of a satellite in a highly elliptical orbit can be over a different part of the planet than your SAM battery.
Assuming all else is equal (same altitude, same targeting capability, same flight characteristics), an interceptor for an 11 km/s target needs about 89% more kinetic energy than an interceptor for an 8 km/s target. Realistically, between the rocket equation and atmospheric effects, the faster interceptor would likely need to be far larger still. You're probably talking about a 2.5 to 3 times bigger missile. While a country that could develop one could likely develop the other if they so chose, it doesn't seem like a safe assumption that a country with one has the other.
If your interception point is say 500 km straight up from your launch point, just to get there you need a rocket that rapidly accelerates to over 3 km/s, and it takes a little over 5 minutes to get to the interception point. To hit an 8 km/s target, you need to fire when it is 2500 km away, to hit an 11 km/s target you need to fire when it is 3500 km away. If to score a hit you need to be within 10 meters of the target at interception, then you need to know the position and velocity of the 8 km/s target to within 4 ppm, you need to know it with an accuracy within less than 3 ppm. And note, if you are shooting from 15 km up in a fighter jet, the 8 km/s target is within your radar horizon, the 11 km/s target is not. Not to say that you couldn't build a system with target sharing and more precise tracking, but it would be a different system than the one you need for the less challenging use case.
Now it's not a strictly either or thing. You could use a missile with intermediate speed and fire it less early. There's a whole continuum of solutions, but it will always be harder to hit the faster moving target. And of course you have real world things to consider like if the target has any maneuverability or countermeasures and how much variation in conditions you can afford. Generally you are already using the best targeting system you can get and are already in the most advantageous position you can be in, so the knob you can turn is "how big of a missile do I need to get the performance I require?"
Dealing with evasion is a whole other matter. A stationary iceberg can hit a ship that tries to evade if it does so too late. Conversely simple error in your knowledge of a ship's position and velocity can cause it to be miles away from where you expect it later in the journey.
The parent is incorrect. You know approximately where it is. If your approximation is off by some amount, you miss. How good of an approximation you have is determined by your detection equipment. How good of an approximation you need is determined by the speed. For the same detection equipment, hitting the faster moving thing is harder.
> I'm struggling to understand the case where you are further from the destination than the x37B, with an orbit 60,000km from earth.
Well yeah, that's because the x37B interception scenario is the second case, where you are much closer to the destination but going much slower.
Again to clarify, no one here is arguing that to intercept a target you have to be moving faster than the target. The argument is you have to be moving faster than the minimum speed required to hit a slower target.
In math terms, you have two targets with velocites V1 and V2. To intercept there is some minimum velocity for each, v1 and v2. This is the best case scenario, you are perfectly in position, you can launch at the earliest possible time. v1 < V1 and v2 < V2 are both true. But since V1 < V2, v1 < v2 is also true. An interceptor that can achieve v1 doesn't necessarily have the capability to achieve v2.