Actually it has been allowed long before 2003.
*** w76 7/15 p. 447 Questions From Readers ***
If a Christian must testify in court, is it proper for him to place his hand on the Bible and swear to tell the whole truth?
There is no Scriptural objection to doing so, though each person must decide whether to comply or to ask to be excused from this.
Honestly, I don't recall a time when Watchtower expressed a notion that swearing on a bible was somehow wrong. But JWs have since the 1950s held a hesitancy to let themselves be placed under oath to tell the truth because of a peculiar aspect of the religion's Theocratic War Strategy doctrine. Old-timers know this and from them the hesitancy has some depth among JWs, but no so much among newer-comers. I recall JWs who didn't want to be placed under oath for simple civil matters because once under oath they feared that unannounced some official might come forth and use the opportunity to ask questions about something they'd rather not give answers to under oath.
And, for readers, it's little wonder that Watchtower took its Theocratic War Doctrine underground because once it put it out there so blatantly in the 1950s law enforcement agencies all over the world were served notice that JWs may or not be telling the truth in response to investigations, that is unless investigators succeeded in putting a JW under oath to tell the truth before asking their questions.