Can "as much as..." be used instead of "no matter how much..."?

As much as is primarily used to say that two things are equal in amount or degree

He likes hockey as much as he likes basketball.

It has a secondary meaning as even though : despite the fact that.

As much as I respect him, I still have to disagree with him on this point.

In this sense the sentence As much as they tighten... can be rephrase as Even though (Despite the fact that) they tighten the shackles, we will never surrender.

But it seems to me still the most appropriate sentence is No matter how much they tighten the shackles, we will never surrender.