One of the great strengths of public-key cryptography is its potential to allow the localization of trust. This potential is greatest when cryptography is present to guarantee data integrity rather than secrecy, and where there is no natural hierarchy of trust. Both these conditions are typically fulfilled in the commercial world, where CSCW requires sharing of data and resources across organizational boundaries. One property which trust is frequently assumed or proved to have is transitivity (if A trusts B and B trusts C then A trusts C) or some generalization of transitivity such as *-closure. We use the loose term unintensional transitivity of trust to refer to a situation where B can effectively put things into A's set of trust assumptions without A's explicit consent (or sometimes even awareness.) Any account of trust which allows such situations to arise clearly poses major obstacles to the effective confinement (localization) of trust. In this position paper, we argue against the need to accept unintensional transitivity of trust. We distinguish the notion of trust from a number of other (transitive) notions with which it is frequently confused, and argue that proofs of the unintensional transitivity of trust typically involve unpalatable logical assumptions as well as undesirable consequences.