I'll slide by for a moment the question of whether corporations should have the right "to petition the Government for a redress of grievances" under the First Amendment and the current extent of this right. Rather, I'll make a point about funding companies at the public trough and whether these companies should be allowed to lobby Congress if they take money.
As a non-profit, my employer faces restrictions on its ability to "lobby" or otherwise engage in political activity. The idea is that we accept this limitation in exchange for exemption from taxes. (It is not a blanket ban, as many suppose, and "lobbying" does not apply to representations before the Executive Branch or the courts.) Foundations are even more limited in their ability to fund lobbying or other sorts of political activity that directly supports a political party as opposed to a platform or issue. (So, for example, Olin can fund CATO to push deregulation, and CATO can say that McCain is better on this than Obama, but Olin can't fund CATO to go out and campaign for McCain.)
So, should we put similar restrictions in place for use of federal bail out money? And if so, at what level? Perhaps we should say "if the feds give you an amount of money equivalent to some percentage of your net worth, we will apply the same anti-lobbying rules to you that apply to Executive Branch agencies." (Agencies may send staff to meet with members of Congress, but are prohibited from "grassroots lobbying" -- making a direct appeal to voters on particular issues.)
I'm reasonably certain that such restrictions would pass constitutional review under the Rust v Sullivan test. The question is therefore whether they are a good idea.