Listing agent says property is income-restricted.

Listing agent says property is income-restricted in Houston, TX and you need to make less than 60k per year to purchase the property. Is this true? Can any home be income-restricted or only in certain areas/states? 

Can you still buy these properties with cash and your own financing (e.g. private family loan) as long as you make under the income restriction (~60k per year)?

NOTE: The property is an under-construction property.

Also, doesn't this mean that the income restrictions will hinder the appreciation of the houses in this sector? What will it take for the income restrictions to lift?