There’s truth in this phrase.
There is no blob of “government” money, or “policy” that can make something affordable for one without making something else less affordable for another.
So if tenants get immediate relief from a rent freeze, where does that money come from?
Those outside the business may think that this will trigger a direct transfer from a wealthy landowner. Structurally this is an impractical notion. Even for those who have equity, it is just that: wealth tied up in the value of the property. It is not cash that can circulate and pay bills.
But in most all cases, the funds that come in from rent are pegged to go out to another obligation. This might be property taxes which are known to increase every year. This might be to a bank that financed the purchase of the property. And the insurance company which provides property isurance as required. This might be to a utility company. Each of these obligations have recourse for non-payment which ultimately leads to their making first claims on the income.
The funds which subsidize the rent freeze are most likely to come from monies intended for repairs and maintenance of the property. These vary from tasks that are good to do but not urgent, to things that if defrayed cause additional costs, to things that need immediate attention like a leaky pipe or a furnace outage. To give an idea of the number of routine items involved in the care of real estate, consider this post.

Over time, two things tend to occur. First, the new landlords with all their positive energy and desires to get ahead can’t maintain a financial foothold and leave. Other longer term owners prioritizes the most important fixes but let the cosemetic upgrades go. Over time more and more of the longer term components age, yards get overgrown, appliances become run down. The housing stock deteriorates.
The neighborhood at large is depreciated by blight, taking a little chunk of equity from every property owner nearby.