Using WordPress 3.5.1 with Multisite, BuddyPress 1.7 and BuddyPress Activity Plus 1.4.1 and I followed the usage instructions to the letter.
I'm using a slightly modified version of RESIZABLE theme from Theme Junkie (with BuddyPress Template Pack) -- and I the BAP buttons don't appear on the activity page.
When I switch theme to TwentyTwelve, the buttons appear, and I can use them.
But when I switch back to my RESIZABLE theme, the buttons don't appear -- though the links shared while TwentyTwelve was active remain in the stream. Disabline all plugins didn't help.
I don't know if this is related or not, but I don't have any EMBEDS under Settings => Media (irrespective of active theme) -- last step in usage instructions.