That's a particularly narrow definition of empathy, most definitions include something like the following:
"the ability to understand and share the feelings of another." [1]
The capacity for this is what helps - it makes it easier to understand how the other person is feeling.
As opposed to compassion:
"sympathetic pity and concern for the sufferings or misfortunes of others." [2]
Empathy is a more general understanding of emotional state - I don't think it's being incorrectly used.
[1] https://www.google.com/search?q=define+empathy&oq=define+em&...
[2] https://www.google.com/search?q=define+empathy&oq=define+emp...
The OP suggested merely leaving open the possibility that your assumptions are wrong. That's really the opposite of understanding, it's expecting that you're not always going to understand, and making space for the other person to explain themselves and make things right.
No - empathy just means feeling the same emotion as people around you, which is not always helpful. What you want is compassion.
I often see "empathy" tossed around as a cure-all for social problem. When someone gets angry at work and it makes you angry - that's empathy. Ever seen footage of a frenzied mob saluting a fascist dictator? That's empathy as well.