This image from the ESA 
prompted the question why the fruits at the bottom left were not floating. An online response claimed after an extended time on the ISS astronauts get used to placing objects in a stationary position. Is there any truth to the claim that astronauts living in ISS "learn" to position objects so they remain stationary with respect to the station itself?
After spending several evenings and going through many dozens of web pages whilst searching for the answer to this question, I couldn't find any definitive claims or quotes that would suggest that such an ability (to regularly place objects at rest on ISS) is common.
In this regard, I believe that it would be very hard to obtain a definitive answer in any other way than asking directly the person on reddit (who was claiming "astronauts tend to get used to managing to put things stationary") what was the exact source of that claim.
Instead, I was able to find many pages quoting various astronauts suggesting that on ISS pretty much everything has to be attached with the use of velcro/magnets etc.
In order to put something steady, it is safe to assume that an astronaut doing this would need to be as steady as possible themselves.
This article, describing importance of person's stability whilst using a sextant on ISS , suggests it's not so easy:
It's especially tricky because astronauts are hardly ever stationary — they float around, so it's hard to stay stable.
I've found two sources citing astronauts who (whilst being in orbit) developed a contrary automatic habit to attach items:
1) An article citing astronaut Scott Kelly:
Even the sensation of gravity holding me in my chair [being on Earth, after the space flight] feels strange, and every time I put a glass or fork down on the table there's a part of my mind that is looking for a dot of Velcro or a strip of duct tape to hold it in place.
2) Although not directly related to ISS (perhaps related to his mission on Salyut station), this article (in Russian) is citing experience of cosmonaut V. Sevastyanov (В.Севастьянов):
Very soon you begin to attach things completely unconsciously, and when you return to Earth, you cannot get rid of this no longer necessary habit for a long time. At one of the first lunches after landing, I suddenly found myself holding a fork, knife, bread, spices and several other items between my fingers.
Original text:
Очень скоро начинаешь закреплять вещи совершенно бессознательно, а вернувшись на Землю, долго не можешь освободиться от этой, ставшей ненужной привычки. На одном из первых обедов после приземления я вдруг поймал себя на том, что одновременно держу в руках вилку, нож, хлеб, специи и несколько других предметов, зажатых между пальцами.
The following articles suggest that everything should be securely attached:
Translated from BBC news article (in Russian):
... most crew members spend the first days on the station [ISS] looking for lost items. All the little things that they use should be fastened with clamps, suction cups, magnets or adhesive tape.
This Roscosmos Q&A page (in Russian) suggests a reason for attaching things:
The movement of astronauts and objects inside the station is affected by ventilation.
This article cites astronaut Sunita Williams:
...you can't just put something down because a couple of seconds later it is going to float away
Article "5,200 Days in Space" by Charles Fishman suggests that
Every single item you use needs to be secured, or it will float off.
and cites astronaut Mike Fincke:
“Keeping track of stuff can eat your whole day,” says the astronaut Mike Fincke—but securing everything also takes time.
Interview with astronaut Andy Thomas:
"Everything floats, which can be liberating but, well, if you're working with tools and you're disassembling a piece of equipment, you can't put anything down."
Even for a temporary stowage, astronaut Sandra Magnus suggests duct tape when describing her cooking experience on ISS:
I cut the onion in half, putting one on the [duct] tape for temporary stowage...
This Roscosmos Q&A page cites cosmonaut Fyodor Yurchikhin (Фёдор Юрчихин):
... it is necessary to attach or fix everything, absolutely everything. Or it will fly away immediately.
So, to sum up, all the anecdotal evidence quoted above suggests that even if some astronauts develop the ability to put objects at rest/stationary, this doesn't seem to be very useful/practical for a long-term positioning of objects.
And if they do, I could think of only two reasons why:
a) to put various food items as close to stationary as possible (for a short time, i.e. few seconds) whilst eating, for their personal convenience, as shown in this video, or for some similar occasions;
b) for fun (as possibly happened for taking the photo with fruits on the table).
P.S. Emphasis added
