So my carbon fibre bicycle is organic? Neato.

I had a friend who was convinced that we had found extraterrestrial life long ago. Not little green aliens. Se just read all those "organic compounds founds", and assumed it was life. So she was casually living in a reality where humanity had found evidence of extraterrestrial life.

True.

We found alkanes.

Looking at Earth, all deposits of alkanes (petroleum) stem from decayed biological matter.

But we think that Earth's first alkanes came from abiotic photochemistry in its primordial reducing atmosphere. Similar processes are abiotically producing petroleum today on Saturn and its largest moon Titan.

Most likely, all petroleum on Earth is tied to life because life has found a way to cycle all non-diamond carbon in our crust, not because petroleum is inherently biological (as you wisely point out).

On Mars, we don't know if generic petroleum that we find is primordial or from decayed life.

Gale Crater is a Noachian crater (early days), and could have gotten filled with whatever primordial goop was falling out of the sky after outgassing during Mars's Hesperian. As Mars outgassed icy elements (CHNOPS) that could not stay bound in rocks that cooled with age, that material would get processed by the atmosphere and end up sedimenting out into sedimentary rocks like Curiosity is looking at. I don't know enough about Hesperian atmospheric conditions to say, but if it were reducing enough abiotic petroleum synthesis could be possible.

Then the only question is whether this petroleum has been cycled by life. Fatty acids are pretty easy to produce from abiotic alkanes by reacting with CO2, which Mars had plenty of. I don't know how these researchers determined that these alkanes likely came from fatty acids (I'm not a petroleum geologist and cannot fluently read fossils), but that alone is not an indication that those fatty acids necessarily came from something living.

However: (judge this harshly)

• Curiosity is looking at sedimentary rocks that it has independently confirmed formed at the bottom of a lakebed
• Fats and oils, rather famously, won't sink to the bottom of a lake
• On Earth, we get oil that gathers with the fossils of life at the bottom of lakes

Oil would float in these lakes, were it not for the life dragging it to the bottom.