Investment income is part of the $4050 limit. So, if the $1451 is his only income, he can still be his parent's dependent if he does not file a joint return (if married) and they provided more than half of his support.
Don't confuse the dependent support test ($4050) with the dependent filing requirement. A dependent must file a tax return if he has more than $1050 of investment income; but he can still be a dependent, because his income is less than $4050.
