I don't think so.
"Rich" refers to a lifestyle that cannot be afforded by just $250k.
An example would be:
- Private school
- Vacation home
- 3+ luxurious vacations a year
- Saving $50k+ per year
- Eating out at fancy restaurants weekly
- Seeing expensive shows weekly
- $1+ million dollar home ($3.5+ million if you're in the Bay Area)