This is the sort of technically ill founded hype that "you know who" takes as gospel true.
Flueless gas fires are not death traps but are subject to a number of rules so that they don't become so. Principally, the power per unit volume is set at a low limit, and additional substantial (100cm^2) ventilation is mandatory. The also have a catalyst to oxide traces of CO to CO2 in the combustion products.
They are much more expensive than basic open flued and balanced flued models of comparable rating.
They have the very big disadvantage that they produce a large amount of water vapour which in some circumstances might be useful in many others will do nothing to reduce any potential or actual damp problems.
They can hardly be described "as breathing life into your room" unless you are a spore of A.Niger.