Earlier quoted context omitted.
It only takes mousing over the button to get an indicator that it can be interacted with. That combined with placement should be sufficient to communicate purpose.
An over-reliance on a hover state leaves tablet users in the dust, though. I see no reason for completely flat buttons, as it's eminently possible to design ones with subtle depth that play well within the bounds of "distinctly digital". The principle that your users need to touch everything in order to learn their boundaries is a dangerous gamble, and may very well be leaving conversions on the table due to risk-ave…
Not only that, it requires a mouse user also to hover over all possible elements to just know what's clickable. Kind of like some of the first graphical adventure games.
Or imagine a website where a link only turns blue and underlined as you mouseover it.
"Input" versus "Indicator" is a big problem in FlatUI that needs to be solved, there is no shared visual language yet to signify which is which, and it needs to be possible by just looking (and preferably other modalities as well)