Are filtered solder fumes safe?

That "filter" doesn't really do anything. The fan however disperses the fumes, which are then ideally vented out by the HVAC system without reaching harmful levels. How safe that is depends on how much air exchange you have and the volume of fumes you're generating.

Edit: I'm surprised this is controversial, but those "charcoal filters" are worthless at removing particulates, which are the primary component in solder fumes. Take a look at the particle size that will fit through them:

Those millimeter-wide gaps are literally thousands of times too large to remove the sub-micron particulates generated by soldering. Activated carbon is more helpful at removing gases, but again, the surface area is negligible and most gases will pass through without ever encountering any surface at all because the filter is simply too thin. If you have one of these, you are depending on the HVAC system to exchange fumes for fresh air. There is a whole EEVBlog episode going over this: https://www.youtube.com/watch?v=ffaiKZMU0Lw

This isn't just my opinion either. Here is a quote from a study evaluating activated carbon foam filters for solder fume extraction:

Activated carbon filters in the form of foams, used with the simpler type of cleaner, had negligible filtration efficiency against either particulates or vapours and would, therefore, offer no protection against any hazardous component of the fume.

Measurement of the Performance of Air Cleaners Against the Particulate Element of Rosin-based Solder Flux Fume

If you can't get access to that ventilation and are going to be generating any serious fumes, then you need a HEPA filter. Otherwise you're just blowing the same particulates in a circle and then breathing them in.

Those generic HEPA filters Dave Jones talks about in the EEVblog videos are relatively inexpensive and they're generally effective (will remove smoke and the order of burning flux from a room), can actually remove particulates, and the filters are interchangeable if you want to buy a name-brand or certified replacement filter rather then trust the generic parts. If you can't work in a well ventilated space, they (at a minimum if not something better) are worthwhile.

In this case, "Safe" is speculative. If you want an absolute level of safety, you want a fume hood or extractor(Could be built into a window with PC fans I would note similar to a drop in air conditioning unit). Carbon filter units like that are the next best option for when a proper extractor is not an option. You would have to specifically analyse the unit in question(how often carbon sheets are changed, quality, total thickness, air flow rate per area) to know exactly what made it through the filter.

As far as different distributions of particulate and gas, there are different alloys of solder and types of flux and soldering temperatures that could account for the distribution, so both of your sources are probably right. If an extractor isn't an option for you and you don't fully trust your engineered unit, it's a very simple device that would be very easy to overbuild. Add a hepa filter, increase carbon filter quality/thickness, make it easy to change and use high static pressure fans to compensate for the additional restriction. How much there was to gain from this would depend on the original engineering, but it's an easy and cheap project.

I use one of those, and the ONLY benefit is that it keeps the fumes and resin plume from rising up into my nose & mouth whilst soldering.

I realize the OP doesn't have this option, but for other readers: I run a 4-inch PVC flexible dust/woodworking tube from the vent to the closest window.

(Image from Amazon, "Ultra-Flex-Clear-Vue-PVC-Hose")