Great points Leolaia! I agree with what you said; well put! ;)
They use this source, Paul L. Kaufman (deceptively it appears), to support their rendering pisteuo eis as "exercising faith".
John apparently uses pisteuo as a verb along with the preposition eis 36 times (according to Paul Kaufman). Verbs have direct objects, and the direct object of pisteuo in these constructs is whatever follows the preposition eis. So, for example, in Jn 3:16, ...whoever believes (pisteuo) in him..., "him" (Jesus) is the direct object.
The WT in their NWT add the verb "exercising" to this verse. However, by adding the verb "excercising" to this verse (...everyone exercising faith (pisteuo) in him...), the verb is now exercising and it has effectively changed pisteuo from being a verb to being a noun; pisteuo is now the direct object of the verb exercising!, and Jesus is now reduced grammatically to an indirect object! It completely shifts the focus.
John uses pisteuo as a verb with an internal action directed on or into Jesus -- the direct object. Mr. Kaufman emphasized this point and said, "i.e. putting faith into someone." When the WT quotes him, this emphasis is lost.
WT uses pisteuo as a noun (exercising pisteuo), making pisteuo the direct object of the verb exercising, and they use Paul Kaufman to support their reasoning. But Paul Kaufman in the actual quote says, "...pisteuo with eis...which should be translated I believe in or I believe on..." and he is actually emphasizing how eis ought to be translated, but the WT hides these facts.
I believe they have quoted Paul L. Kaufman in a horribly dishonest way.