I´ve reviewed my notes and technical docs about this. Didn´t remember exactly how was it meant to be.
The input impedance is not an absolut impedance (just as I explained in this thread). That value (140kOhm) is a value measured in a test circuit which has a secondary impedance of 1kOhm. This is, a step-up of 140:1, aprox. That´s a measured impedance in that circuit, applying a 1kHz signal at 0 dBu. The theoretical value of "squared turns" is an aproximation, given the impedance varies a little depending of frequency and amplitude.
That´s why Radial (or Palmer or Whoever) states that impedance. It´s just an inaccurate way of giving the info, which nobody will care, by the way.
At the same time, the stated output impèance of 150Ohm is measured in a test circuit that "aprox simulates" a guitar pickup. They remove the 1kOhm impedance of the previous test, and just measure the resulting impedance.
You can see that in this pic, from the Jensen official specs. The circuit 1 is the one used to measure those impedance values:
So, yeah... Manufacturers just give a value that can be misleading because they don´t tell the full story.
Everything is as I explained before. With a passive, transformer based, DI box, if you´re connecting the output to a preamp in the 2kOhm ballpark, you´d maybe notice the lack of higher impedance (you´ll be around 250-300kOhm). If your preamps are a bit higher impedance, you´ll have great respose. My DI boxes behave excelently in that regard when connected to a mic preamp in Behringturd X32 mixers (as an example), because they´ve got higher impedance than other preamps. Connecting a strat and comparing it to other boxes, playing clean you notice all the bright frequencies of the pickup. I didn´t compare it to a Radial (We had none). But compared it to a Palmer, a Behringturd and a couple Milleniums... mine kept more frequency content, while being the least noisy (maybe tied to the Palmer). The transformer is everything in these boxes. My buddy calls it "the Radial" when he talks to other guitarists about the box... even though I told him 10 times it has a cheaper transformer (well, it´s a 50€ made-in-the-UK one, not a chinese cheapo). He just feels it great and don´t care for technical details.