Button drivers generally set a flag on the event that causes the platform to treat the event as a state change, even if the old and new values are the same. If it didn't, apps like Button Controller would also fail in a similar manner.
First, I'm able to reproduce the failure with a rule like this--it only triggers if the value truly changes, not on any event that comes in (as may often be the case without a change for buttons that use isStateChange: true for the event):
I thought it used to work like that, but I just downgraded to 2.3.0 to test, and it seems to work the same way there, too, so I'm not really sure (but I'm also pretty sure this exact setup has been recommended for odd cases like these in the past).
Second, it's not clear to me if the UI should allow "**Any Value**" here or not; I know this has use in the "Time Since Event" condition, and I suppose it could be useful for sticky triggers when you just care about a change but don't care what it is, but then I'm not sure why it's prompting for a specific value (or how that's different from "**changed**" if it shouldn't), so I'm probably just missing something or this is a UI oddity.
Both of these are good questions for @bravenel. (To expand, the second issue appears when using a Custom Attribute trigger, here a button and the "pushed" attribute, though with some playing around I did, it doesn't seem to matter.)
In any case, since 2.3.1 is done, you'll be waiting at least until 2.3.2 for these changes, so creating either multiple triggers or using a custom app that subscribes to whatever might be the best idea in the meantime. (Or perhaps clone and edit an older Rule version if you can find one that works the way you want, but I just tried all the way back to 4.1 and it does the same, so my memory must be way off here...)
What you're showing is a UI glitch that I will track down (where the UI puts a value in parens as part of the trigger).
If you use *changed* as the attribute value, the resulting subscription is for just pushed. This would contrast to subscribing to pushed.1 to get a subscription to button 1 pushed. This is what you said you were looking for.