this is complete not true!You need to be either (a) a US citizen, or (b) a US Permanent Resident (ie. green card holder).
As a green card holder myself I recall I had to wait about 6 months before I could even apply for the Texas CHL.
Once you have the CHL, it certainly does make purchasing firearms easier, though, as a side note... being a green card holder, you would still have to produce your last 3 utility bills to purchase a firearm. Utility bills means either water or electricity bills in YOUR name and showing YOUR CURRENT address. I don't know why they have this stupid requirement but it's part and parcel of making a purchase.
I don't know much about your particular visa but if you don't have a green card then you can't get the CHL in Texas.
BTW, I'm originally from the UK where even carrying a 1" pocket knife will land you 5 years in jail.
Immigration status never is the requirement for CHL!