by pjohnmeyer on Tue Oct 09, 2012 10:15 am
803.04 E:
"If a large solid obstacle prevents a player from taking a legal stance within 30 centimeters directly behind the marker disc, the player shall take his or her stance immediately behind that obstacle on the line of play. The player must comply with all the provisions of 803.04 A other than being withing 30 centimeters directly behind the marker disc."
That would apply if the picnic table made it impossible for you to take your stance and throw legally. Sadly there are lots of openings in a picnic table and so this probably doesn't apply.
803.05 A includes the part you mention about the picnic table -- it even specifically calls out picnic tables.
"No relief is granted from park equipment (such as signs, trash cans, picnic tables, etc.), which is considered part of the course."
This part in bold is important, because the TD could declare picnic tables "casual" obstacles under 803.05 B if he or she so chose.
But, assuming the normal rules hold and the picnic table is in play, you can choose the optional rethrow as you mention, but you can also choose Optional Relief under 803.05 C. While it does still incur a penalty throw, the lie "may be relocated to a new lie that is no closer to the hole, and on the line of play." Much better than re-teeing.