The first answer is that it really doesn't matter about the "details of any diving" - what matters is that you have recently been diving. I suppose you could just air up at the shop and go out and let the air out, write lies in your log and then fill it up and have them stamp your bogus log. Any kind of stamp will do - I even get a stamp that is their address stamp. I also have received a letter from my PADI shop that stated they knew me and my recent diving. And I still needed my log book.
Also, unlike the USA, all divemasters, instructors, and dive shops must be certified by the Israeli Dive Authority (IDA). All incidents are reported to them and the can and will pull the shop's license and individual's privilege to dive in Israel. Therefore, the shops maintain careful records when you dive with them. They also keep your certification cards and dive insurance/DAN cards (required to dive in Israel) in their shop when you dive with them. They must be able to present them to IDA on request.
You obviously have not been diving in a bureaucratic country where there is strict enforcement of laws. Regarding solo diving, the local dive professionals will notify the Israeli Dive Authority, who will confiscate your gear, take you to the local police station, and what comes after that will obviously cost you lots of money. If you are upset about the "solo diving laws" - go to to ScubaBoard's solo diver site (which both you and I are members of) and you will read about the enforcement, including hefty fines for solo diving in places like the State of Washington's dive parks.
Anyway, the op was asking about why to keep a log. I simply reported a country that requires a log for one to demonstrate a recent history of diving. Obviously the issue is with the Country of Israel (and likely other countries and locations) and not with me who reports such laws.
A note about Israel. It is the most Northern coral sea - and it is beautiful. There are a lot of tourist divers from many countries who do not dive on a regular basis. The IDA is out to protect them and the environment. Just South of Eilat is Egyptian territory where the coral beds have been torn up by sticky fingers. In the Israel Red Sea, only divemasters and above are allowed to carry dive knives or allowed to wear gloves!!! This is to protect the coral from tourists who just cannot keep their hands off and would love to take souvenirs. One is also required to attend a lecture by a park ranger to dive in their sanctuary. Anyway, sorry to go on and on - I'm just answering to the op that there are places that require a log.
drdaddy