According to RebelNews, Canadian MP Anthony Housefather said
It's because these documents were signed at the beginning of the pandemic when everybody was desperate for vaccines, when companies were being told to rush vaccine production, do testing in an unprecedented way, a way they normally don't do it.
So these companies were exposed to way higher liability putting their products on the market on the market than they normally would because they didn't do the type of testing that normally takes these drugs years to come to market. They did it all in less than a year.
So that's why these companies said, ‘if I'm going to deliver you this product that I haven't tested in my normal way, I want to have different conditions’. And with countries all around the world competing with each other to get these, the countries had less leverage than they normally do.
The last sentence (after the emphasized one) can easily be checked out to be true, e.g. some of the EU countries did that according to a "Special report [on] EU COVID-19 vaccine procurement":
The Commission and Member States considered early introduction of the vaccine to be in the interest of public health. Member States were therefore willing to reduce manufacturers’ risks linked to liability for adverse effects. This was intended as a risk-sharing principle in the vaccine strategy. While respecting the general principle of liability under the Product Liability Directive, the provisions in the contracts concluded with COVID-19 vaccine manufacturers differ from the pre-pandemic practice as Member States have taken over some of the financial risks normally assumed by the vaccine manufacturers.
What remains in a bit of doubt is if the highlighted sentence (in the 1st quote) was the main reason invoked by manufacturers during negotiations in asking for reduced liability, rather than being a more subtle allusion, which e.g. Reuters quotes the manufacturers association as being rather more vague in public:
The industry trading body, Vaccines Europe, said it was working with relevant authorities to agree a system of compensation that would avoid “endless delays through prohibitively expensive litigation with uncertain outcomes”. [...]
The EU stance on liabilities could partly explain why, despite having a bigger population than the United States, it is lagging Washington in securing potential COVID-19 vaccines.
The U.S. system shifts liability for vaccines fully to the government and shields drugmakers because widespread inoculation against disease is considered a benefit to society.
So, is there more direct evidence that's what the vaccine companies said in negotiations, i.e. they explicitly invoked the testing schedule as a reason (as opposed to e.g. making a comparison with other jurisdictions)?