Limiting rentals [TX][SFH][board member]

The subject of limiting the number of rental homes in our 121 unit HOA came up last night. One of our board members is passionate about property rights and opposes any attempt to curtail rentals. I have heard from more than one source that if there are too many rentals in a given neighborhood that certain types of loans will not be written. Can anyone point me to a source of that information? Our reluctant board member is demanding proof. I suspect we are getting close to being 30% rentals.