Yes, there will always be a need for trust, and Bitcoin doesn't change that. What it does is actually facilitate more, rather than less, trust.
By having a rock-solid form of money with a well-known, immutable monetary policy and issuance rate, that doesn't rely on any single entity and is very difficult to corrupt, all kinds of trust-related issues (moral hazard, Cantillon effect, theft of purchasing power) are resolved.
In addition, commerce and exchange between strangers can more easily be facilitated based on such a system rather than one that relies on multiple intermediaries.
If I can have cryptographic proof of escrow in a multi-sig wallet (2 of 3, where there is a trusted (!) 3rd party), I might be willing to do a transaction with someone I might otherwise not (e.g. due to a lack of trust that they have the funds available).