Yes I found this pic of Dubinina using this 2-man saw whilst trawling through the site. Could have been at Ivdel.
The fact that there was a saw also mentioned in the inventory that you posted too at the bottom of the list.
It was also mentioned maybe by the rescuers that the tent floor was well organised and an Ice-axe ans saw were found by the entrance.
Credit where credit due.
Perhaps they didnt see the saw.
I believe your picture is from a previous expedition and not the 1959 .
Here is another photo with one of the saws in it . It's in the middle standing vertical next to the tree . At least I think it's a cross saw.

What we know is they took some things of their own and a bunch of equipment from the UPI . This equipment was signed out and was to be signed back in to the stores. A saw was counted out and the saw was found in the tent.
The location of the equipment and items found in the tent maybe not exactly as they were left at the time of the incident because the first searchers did move things.
The stove can be used in bad weather if needed and it can be taken down if needed. The speculation about the log found was that it was a log specifically prepared from the day before , a dry log which they use to get the next fire started . It may have also be getting saved for a morning start , one log cut into kindling would be enough to take the worst chill away from the tent and get dressed and ready for coming day . It may also be useful to thaw the tent a bit to help for packing but I'm not sure about this , it may make things more difficult. I have not hot tented with canvas below -8c.