With a 1 series body all points are high sensitive with lens of f/2.8 or faster
It's important to distinguish between accuracy and precision. Accuracy is 'closeness to true' whereas precision is repeatibility. So, a system can be accurate but imprecise (meaning you get the right answer on average, but any one measurement can be way off), or precise but inaccurate (meaning you get the same answer every time,but it's wrong). Here's a diagram that illustrates the difference:
An f/2.8 point is more accurate than an f/5.6 point, because the baseline is wider. The f/4 center line in 1-series bodies achieves the same accuracy by using a sensor line with twice the density of 'pixels'.
The center point on most Canon bodies, including the 1-series, are 'high-precision' AF points. That specification means that point is precise to within 1/2 to 1/3 of the depth of focus for the max aperture of the attached lens, depending on body (depth of focus is the sensor side equivalent of depth of field, it's measured in µm in front of/behind the sensor). Other points that aren't 'high-precision' are specified to be precise to within one depth of focus.
The issue gets confusing because Canon's marketing literature often fails to distinguish accuracy from precision, using the two terms as synonyms (not uncommon in lay speech/writing, but IMO poor practice in technical documentation). I clarified the issue for myself in an email exchange with Chuck Westfall.
A cross-type point just means the point is sensitive to phase differences in two orientations - it means achieving a lock is possible with more kinds of subjects. Being 'cross-type' says nothing about accuracy or precision of the AF point.