Bitcoin only gets its value from scarcity if you look at it from the context of a traditional currency.

It's volatile because there is a lot of speculation going on; there is a lot of speculation going on because nobody has figured out how to value it against a traditional currency yet (in other words: speculation transactions outweigh productive transactions e.g. the proverbial alpaca sock).

While there is scarcity - and said scarcity is driving speculation - the intrinsic value of btc derives from the cryptographic trust in the validation of the Bitcoin blockchain, and the promise that a btc will always be accepted as a bounty on the validation of a btc transaction.

It's fundamentally different than the promise inherent in traditional currency: that a unit of currency must be accepted for the repayment of debt. Instead, a unit of currency must be accepted as a bounty on the cryptographic assurance that a transaction is not fraudulent.

What defines trust in a system, and when does that come in to play in the valuation a system?

With a satoshi sent to an address that cannot spend its balance along with the cryptographic signature of a document, you can execute a proof of existence. Distributed, mathematically validated notary.

It can also be used as a decentralized, trust-based escrow system.

The value inherent in a single btc is more abstract than a brick of gold, and has more to do with Bitcoin itself.