The down round theory doesn't really make sense. Let's say you own x% of a $y car, but you have the power to crash it and write it off (at which point it is worth $z for parts, z << y) with no consequences except the loss of value in your share. If you do it, after the crash, you can buy any percentage d% you don't already own in a down round (0 < d < 90), at the current price, $z/100%.
Before the crash and down round, your interest is worth $(y * x/100). After the crash, your interest is worth $z * (x + d)/100%, but you have to pay an additional d%/100% * $z. Therefore, the crash and down round changes your wealth by $z * (x% + d%)/100% - $(y * x%/100%) - d%/100% * $z = $(z-y)*(x%/100%). Since z << y, and x > 0, the VC will always lose wealth by destroying value to force a down round. If they could get a z value higher than the true value, the situation might, change, but that would be difficult.
What I think is actually happening here is the VC is playing what is called a game of chicken in game theory (http://en.wikipedia.org/wiki/Game_of_Chicken) to try to get more than their rightful share of the deal. A game of chicken is where if one player gives up first, the player who gives up loses a small amount, and the other player gains a small amount. If neither player gives up, they both lose a large amount. The VC wants you to give them more, by forcing you to choose between doing what they want, or hurting both yourself and them by completely destroying value in the company.
Strategically, you now need to either capitulate to what they want, convince them that you won't back down (if they are convinced you won't back down no matter what, it is in their interests to back down and let the next acquisition opportunity go ahead), or find a way to stop them blocking acquisition.
Before the crash and down round, your interest is worth $(y * x/100). After the crash, your interest is worth $z * (x + d)/100%, but you have to pay an additional d%/100% * $z. Therefore, the crash and down round changes your wealth by $z * (x% + d%)/100% - $(y * x%/100%) - d%/100% * $z = $(z-y)*(x%/100%). Since z << y, and x > 0, the VC will always lose wealth by destroying value to force a down round. If they could get a z value higher than the true value, the situation might, change, but that would be difficult.
What I think is actually happening here is the VC is playing what is called a game of chicken in game theory (http://en.wikipedia.org/wiki/Game_of_Chicken) to try to get more than their rightful share of the deal. A game of chicken is where if one player gives up first, the player who gives up loses a small amount, and the other player gains a small amount. If neither player gives up, they both lose a large amount. The VC wants you to give them more, by forcing you to choose between doing what they want, or hurting both yourself and them by completely destroying value in the company.
Strategically, you now need to either capitulate to what they want, convince them that you won't back down (if they are convinced you won't back down no matter what, it is in their interests to back down and let the next acquisition opportunity go ahead), or find a way to stop them blocking acquisition.