Sen John Kerry hits back at veterans' group that has mounted massive campaign to discredit his Vietnam service record; says their claim that he lied to win medals is categorically false, and claims members of group, Swift Boat Veterans for Truth, are tools of Bush campaign; his decision to take on group directly reflects how prominent group has become in last few weeks as it advances its cause in book, television advertisement, and on cable news and talk radio shows; group came into existence because of members' longstanding anger about Kerry's antiwar statements in early 1970's; records show group received bulk of its initial financing from two men with ties to Bush family, as well as web of connections between group and high-profile Texas political figures and Pres Bush's chief political aide Karl Rove; close examination shows group's accounts of events to be riddled with inconsistencies, in many cases undercut by official Navy records and men's own past statements supporting Kerry; several group members who now declare Kerry 'unfit' have in past lavished praise on him, some as recently as last year; excerpts of some of their statements; detailed examination of charges and facts in case; chart showing relationships of group members with close Bush associates; photos (L)