This article presents standard error as the quantity representing "by how much our prediction could be off" without mentioning that this is only so for a single

This article presents standard error as the quantity representing "by how much our prediction could be off" without mentioning that this is only so for a single standard deviation. For a normally distributed value, one standard deviation only covers around 68% of the cases so you'd have to at least double that error value if you want to be pretty sure of your conclusion (which would then cover around 95% of the cases).