Your numbers aren't adding up. According to the article - "Jackmon said her group operates an application portal for people applying for rental assistance. However, she said, “We had to close the application portal because we currently have over 7,500 applications (and) we only have $9.6 million.” Each week, she said, 50 eligible applicants are randomly selected based upon geographic and income criteria. The highest priority is helping those with the lowest incomes, she noted. The maximum amount a family can receive in one year is $6,000, with the average assistance at about $4,200, Jackmon said."

I can't find the exact numbers of renters in Austin, but one website says there are 440,000 homes in 2020, and another says that about 48% are renters. Wikipedia says there are 2.28 million people in the Austin area. Regardless, giving 50 families extra money every week would in no way cause market rates to rise. That's preposterous. This is such a miniscule amount it would in no way affect the value of that many other rentals. Besides, in your supposition, you are saying that the landlord findsout about their tenant getting an extra $300. Well, again, how would they know that? The tenant could make $300 in any way that would be unknown to the landlord. Sorry, but your argument just isn't holding water with me.