Radars versus stealth
The remarks about "low visibility" are correct - no aircraft is totally invisible to radar (or other detection methods, including sound and infrared). However, it is the degree of diminished effectiveness that matters. If I can effectively reduce a radar's detection range of my aircraft from 200 NM to 20 NM, I have a better chance of finding an uncovered path through an enemy's radar perimeter. Yes, I may need to adjust as I go, as some radars are portable and that gap may not be.
But the key point that needs to be born in mind is that it is easier to build sensors to test a stealth/low visibility design than it is to build a stealth/low visibility target to test sensors. Radars, as an example of a sensor, are comparatively simpler (and that is one of their strengths) when compared to, as an example of a stealth/low invisibility platform, a fighter/attack aircraft. For radars, I can alter broadcast (continuous wave, phase array, etc) and frequency and power - a large enough test stand can examine a number of these variables in various combinations. It is almost impossible to give a particular radar a similar variety of airborne platforms to test against.
Given that the capability of all operational radars are known (there is no such thing as a "stealth" radar - once it begins broadcasting, its variables become readily known, which is one of the prime roles of surveillance aircraft. For a good account of the detection-change struggle for radars, see books on the Battle of the Atlantic by Morrison or Overy or others), then it is reasonable to assume that the designers of the F35 tested their platform against the large numbers of radar types available or projected to be available by potential adversaries. They did much the same with the F117 prototypes. The results of such tests have an impact, as has been at least implied by several earlier comments, on the tactics that are adopted.
For example, it may be the F35 is detectable by radar system A at 150 NM (but can see an F15 at 250 NM) and the enemy uses system A to oversee the battlefield which holds numerous targets that the force commander would like to address using the F35; on the other hand, system A can only see a B2 at 20 NM. On the battlefield, the enemy uses system B which, while movable, cannot see the F35 beyond 20 NM. Then the tactic might be to have the B2 kill any system A radars on its way over the battlefield while going after deeper targets, thereby opening up a path for the F35s. Using antiradar missiles with ranges well in excess of 20 NM, the F35s kill the system Bs and go on to deal with targets in the battlefield itself. The destruction of the Bs permits conventional attack aircraft to be used (F16, F15E, Typhoon, etc) for an even greater portfolio of targets. Again, this is nothing more than an example.
One other comment - the Foxbat was initially presented as the aircraft for which the West had no response. It's thrust was so great that no aircraft could turn with it, much less keep up. I still recall the classified presentation on the subject to my fighter group and the disbelief that many aircrew (we were a Phantom outfit) expressed. The briefers, as it turned out, were wrong and the aircrew were right. But that was the Cold War and the penalty for being wrong could have been utter disaster.