Readers are referred to the previous blog article for the general details of how transport in the Helsinki area is organised and for the meaning of the 0, 1, and 2 options. They were correct.
What wasn't correct was the information about the new L and 3 buttons which was taken directly from a short information piece in the main Swedish language paper (in Finland) Hufvudstadsbladet (Hbl) using information issued by the Swedish language branch of the Finnish press bureau.
What seems to have happened is that the Swedish language branch of the Finnish press bureau translated a piece of information issued by the regional traffic authority incorrectly and Hbl in picking up the translation rather than looking at the origional text made public this error.
The reason I was able to spot this was that two days later, the main Finnish language paper (Helsingin Sanomat) printed half a page (with pictures) on the same subject. They of course were able to use the original news release and so we see that -
the L option is for travel in the "local area" (i.e. travel from and too any of Kerava, Vantaa, Espoo(incl. Kauniainen) and Kirkkonummi) that doesn't include Helsinki. Nothing to do with trains at all except for travel within Kirkkonummi where this "ticket" is restricted to train travel only (in Kirkkonummi)
the 3 option is then for travel within those same (L) areas but which also incorporates travel within Helsinki.
Perhaps more interesting is to how this mess-up in information came about.
The Finnish text says
L käyttävät Espoossa, Kauniaisessa, Vantaalla, Keravalla and Kirkkonummen junaliikenteessä.
or
L is used "in Espoo", "in Kaunianen", "in Vantaa", "in Kerava", and "in the trains of Kirkkonummi"
(note that "in Espoo" is one word in Finnish)
This is very clear - in the trains applies only to Kirkkonummi because only there do you have "of" before the name of the area.
The Swedish faulty "translation" (as used by Hbl - but using Finnish placenames in my translation) was however
Med L-knappen kan man köpa en värdebiljett i tågtrafiken i Esbo, Grankulla, Vanda, Kervo och Krykslätt
or
With the L button you can buy a "value ticket" in the train traffic in Espoo, Kauniainen, Vantaa, Kerava and Kirkkonummi.
Here, there is a restriction to trains for all the areas.
Yet another case of "you can't believe what you read in the papers". Some people don't take both newspapers so will be stuck thinking that L is only available in trains.