Should I print in a well ventilated area?
The short answer is: yes, it is always a good idea to print in a well-ventilated area.  The longer answer can be articulated as follows:
Definition of &quot;fumes&quot;
&quot;Fumes&quot; is a fuzzy word that from a chemical/physical perspective includes at least three different things:

Vapour - the gas phase of a substance
Aerosol - a airborne suspension of tiny particles of liquid, solid, or both
Smoke - particles and gases emitted when a material undergoes combustion or pyrolysis (so really: a smoke is a combination of vapours and aerosols too... but the combustion/pyrolysis will have changed the very nature of the material, so it will be &quot;vapours and aerosols of a different substance&quot;

Interactions with the human body
Each of the above has a different way of interacting with the human body.  The list of possible interactions is huge, and out-of-scope for this answer, but just to mention a few obvious ones:

Vapours tend to enter cells by osmotic pressure and can have carcinogenic effects by either attacking the genome of the cell or by disrupting its metabolic processes (think: benzene in car fuel)
Aerosols can trigger the immune system, and in return have the body develop allergies or autoimmune reactions.
Aerosols can deposit their particles on the cellular membrane, making it impossible for it to operate correctly and eventually fail (like neurons failing to transmit electrical impulses, for example)
...

Composition of filaments
Modern filaments are a combination of different substances: the basic plastic (PLA, ABS, PETG...) that gives the name to the filament is almost always mixed with other plastics and additives that change its physical characteristics.
In some cases, the filament is host to particles of other materials (like wood, metals or phosphorescent compounds).
Each of the different materials have different transition and critical and flash points (the temperatures at which they will become vapour and ignite respectively), and different physical properties which in turn will affect differently the size of the particles in the aerosol coming out of the printer.
Conclusion
The bottom-line is that it is close to impossible to have a complete understanding of how a given &quot;fume&quot; affects human health.
Typically the safety of a substance is tested in a lab by directly observing its effect on cells, or by performing epidemiological studies in a population, if the exposure data to a given substance is known.
When people comment on PLA being &quot;safe&quot; for example, they typically refer to studies that tested inert, cold, chemically pure PLA.  But the fumes of a PLA filament will probably not be inert, nor cold, nor be exclusively PLA.
Additionally, it has to be observed that it is much easier to rule a filament harmful than safe: for it to be considered harmful it is sufficient to know that one of its components is harmful (for ABS that is typically studies showing the adverse affect of ABS aerosols on health).  For it to be deemed safe, one must know that all if its components are safe, but most filament do not go through the rigorous testing required to ascertain that.
In conclusion, it is always a good idea to get rid of the fumes from 3D printing regardless of the type filament being used.  The ideal solution is a printing enclosure maintaining negative pressure, but an enclosure with air filtering or a well ventilated room are also good options (ventilation can have adverse effects on printing quality though, due to drafts and their cooling effect).