She gave you incorrect information. Just one of many examples would be a Rinnai. Itís a Category III vented appliance with models that put out up to 38,000 BTUís. Most whole house furnaces and boilers are rated between 80 and 140,000BTUís so a Rinnai is powerful and efficient.
Itís my professional opinion that Unvented heaters arenít safe. Combustion gases should never be allowed to remain in your living space. You wouldnít park your car in the living room and let it idle while you sat on the couch watching tv.
My personal inclination (not as a professional but just a lifetime of experience burning and heating things) matches with yours.
However, lots and lots of companies sell lots and lots of people "ventless" heaters that are used to heat houses all the time, within all the usually-overly-tight building codes, and I don't hear about people dying from them very much ....
I looked at the Rinnai heaters and realized that I'm not just talking about a heating unit; I'm talking about something that would take the place of the fireplace, with a visible and possibly less-efficient flame, but which would put out a reasonable amount of heat via fans and/or heat exchangers ....
So maybe I'm asking too much of a system.