That word falls under the group of words I like to call "Photoshop Words"
"Photoshop Words" are nouns that are commonly used, incorrectly, as verbs.
I call them "Photoshop Words" simply because photoshop is the most common noun used as a verb.
"Just photoshop it out".
I think webcasted is a perfectly acceptable way to use webcast.
Now... graciously accepting... that's just conceited...
