True.
However, I believe it was "Brew Like A Monk" that let us know that they do share the same strain of yeast.
That's not the BLAM story.
Westvleteren brewed in-house from 1838-1946. They then outsourced, and St Bernardus brewed Westy from the late 1940s until about 1992 on a contract basis. At that point, Westvleteren started brewing in-house again (they were told they couldn't use the Trappist logo unless they actually brewed in a Trappist monastery; Achel actually lost their Trappist status around this time for several years until they moved brewing operations in-house).
When Westy went in-house, St Bernardus kept the original yeast and recipe. The new Westvleteren uses Westmalle yeast--they actually pick it up from Westmalle every brew day. Achel also uses Westmalle yeast.
So St Bernardus Abt 12 is the same recipe and yeast as the pre-1992 Westvleteren 12. All Westvleteren 12 produced since moving back within the walls of St Sixtus is a new recipe and yeast.
Westvleteren 12 was introduced in 1940, so it's been brewed by St Bernardus for 36 years (not counting the post-1992 St Bernardus Abt 12 beer that uses the traditional Westvleteren recipe) and by St Sixtus for 24 years.
Because both the recipe and yeast have changed, you have to know the date of reviews-e.g. all those classic pre-1992 Michael Jackson reviews are praising what is now called St Bernardus Abt 12, while newer reviews apply to the reformulated St Sixtus-brewed Westvleteren 12.