Not true. The transaction has to be verified by multiple other people before it can be trusted. If you spend the same bitcoin twice in a short time period, it's a toss-up as to which one gets accepted into the official blockchain.
>The transaction has to be verified by multiple other people before it can be trusted.
That's not how it works, sorry. If you don't double spend your transaction and you attach a proper fee it's going to get in the chain, period.