For MLB, IIRC the only exception is for Sunday night games on ESPN. All other national games are non-exclusive: while ESPN/TBS/Fox are broadcasting it nationally, the local stations are broadcasting as well, which can be streamed through the mlb.tv package. Sunday nights are the only games that are national-only, and so can't be streamed through mlb.tv.

Once the playoffs start though, all games are national only, and there are different rules, making the playoff games more difficult to stream.