You apply Occam's razor to rule out that the source of a thread came from man made elements that have landed in the area recently so you can rule in that a fungus survived a direct hit from a meteor, was blown into space, just happened to intersect mars, survived martian atmosphere for hundreds of years and just happened to be where our rover took a recent picture. Nice, very nice.
Fungi spores are quite robust, and, due to their incredible lack of mass, would float gently to the ground rather than burn up during descent. As to being freeze-dried in space before landing, I doubt that would be too much of an issue for at least some spores of some fungi types.
Finally, they are ubiquitous in earth soil. Any impact of sufficient ferocity to send them into space would doubless succeed, since they're everywhere it might have struck.
Since you challenge this relatively common-sense theory, please let me know what type of "thread" that "came frome man made" sources would have the same appearance of a fungal thread (varying taper, not "corkscrewed" due to having been a single fiber twisted into a thread and woven into fabric), and, the process that would present them on the surface where they've been found -- without also leaving more obvious fabric artifacts visible (i.e., tattered threads (made of groups of fibers), torn patches of fabric, etc.)
Ball's in your court. Before you answer, you might want to look at some photomicrographs of various fungal threads, and do some reseach on the durability of fungi spores.
Lets assume the a million to one odd's that the event occurred and sent the fungus to space. I'd like to hear your thoughts on the chances that the trajectory of something like that would intersect mars.
As far as the ball being in my court here is what you need to establish with Occam's razor no less
1. A meteror that evaporated on contact would send debris containing a fungus into space. (Maybe what ? 1 in a 100,000?)
2. The heat from the vaporized meteor would not kill a living thing in the vicinity ( Maybe what ? 1 in a 100,000 ?
3. The debris containing fungus left with sufficient force to completely leave earths gravity ? (Maybe not even physically possible but lets give it another 1 in 100,000).
4. Now the debri that contains a fungus, which avoided getting vaporized, which was blown off the earth, which had enough momemtum to leave earths gravity, AIMED itself directly to intersect Mar's orbit on the same plane in space that Mar's is revolving on (Okay, it takes our computers and men many days to calculate the course but this series of events got it just right in a chance that has to be in the 1 in a trillion neighborhood, but lets give it 1 in a 100,000 to be fair. But there is more.
5. The debri that contains a fungus, which avoided getting vaporized, which was blown off the earth, which had enough momemtum to leave earths gravity (is that about 1/2 way to moon?), that AIMED itself directly to intersect Mar's orbit intersected on the very same plane that Mar's is orbiting intersected the orbit at the very same moment that Mar's was passing by.... (Another 1 in a 100,000 ? ) but there is more.
6. In addition to surving its collission with Mar's it settles down in the very same tiny small area that our Rover is sent to take pictures (Another 1 in a 100,000)
7. Only one more to go. This same rover assigned to investigate a small patch of a planet happens upon a very small fungus which managed to survive in an alien environment and made it into one of the first photos. Another 1 in 100,000.
Thats 1 chance in 100,000,000,000,000,000,000,000,000,000,000,000,000,000 give or take a few.
This has got to be the all time record for the wildest use of Occam's razor.