It isn't 'well below median income'. It's a 'percentage of the poverty guideline' which is different in each State.....
The Federal Poverty Guidelines are used to calculate whether you qualify for legal aid, public benefits, and other services.
texaslawhelp.org
Also, the amount of people per household is THE determining factor, not (just) income. A family of 3 with an income of $50,000/yr. might not qualify, but a family of 6 might. There's also the matter of some income NOT being included in calculations, like child support and SSI/SSD.
A LOT of people think like you do and don't even bother applying. Others are just embarrassed. My advice: apply, the worst that can happen is that you're denied.