SS

If you have combined income that exceeds $25,000 as an filing single taxpayer or exceeds $34,000 if married filing joint, then yes up to 50% of your social security income "may" be taxable.   It is dependent on all the income your have, whether wages from a side job, self employment income, interest, dividends and capital gains. 

What you say you were told is not true. As icalvo said, how much of your Social Security is taxable depends on your other income. If Social Security is your only income, you do not pay tax on any of it, no matter how much it is.