Folks that use supply and demand principles to argue against UBI don't seem to understand themselves.
If everyone is given $1,000/mo, it does not necessarily follow that living costs will also increase by $1000/mo. For that to happen, the additional $1000/mo would need to actually increase everyone's demand for services, which is generally not the case. Having more money generally does not make you want something more, it just makes it easier to afford it. If more people can afford something and start purchasing it in greater numbers, then yes, the price will increase, but they are also getting something the thing of value in return.
Put another way, giving everyone $1000 will likely increase prices, but the increased prices will be less than $1000.