Does the word "since" ever have a meaning of "thus", "hereby" ones?

Here is a sentence from "Programming Perl":

They [constructors mentioned above in the book — OP's note] don’t really care whether they were invoked from tie, nor do any of the other methods in the class, since you can always invoke them directly if you’d like.

In my dictionary since is translated only as "because", "from the time when" etc. But it appears to me that in this sentence since is a synonym of thus, as "you can always invoke them directly if you’d like" is the consequence of the first part, rather than the cause of it.

Is my assumption correct?

I dont think the sentence is a result clause that should be prefixed with thus. Since is used correctly and means because. Here is how I get it:

They don’t really care whether they were invoked from tie, nor do any of the other methods in the class, since you can always invoke them directly if you’d like.

The italicized part serves as an additional info for the first clause and could be dropped without losing any meaning.

They don’t really care whether they were invoked from tie, since or [because] you can always invoke them directly if you’d like.

Is your assumption correct? That depends on which assumption you're referring to.

One of your assumptions appears to be that thus and because cannot be used interchangably, that because is used to indicate causation, and thus is used to indicated consequence. And then there's a second assumption, that the word since should be used only as a synonym for because, but not for thus.

I have no problem with the sentence as written (neither did the publisher, apparently). Since the sentence appears to be okay, we need to figure out where the erroneous assumption is.

I think the line between cause and consequence is a blurry one:

The egg broke because I dropped it.
I dropped the egg; therefore, it broke.

I also like the way Macmillan wrote their definition of since:

used when explaining why someone does something or why a situation exists

This definition keeps the word versatile; without a constraint that the word can be used as a synonym for because, but not thus (or vice-versa). That's more in line with how I've observed the use of these terms:

I had to pay a fine because the book was overdue.
Because the book was overdue, I had to pay a fine.
The book was overdue, so I had to pay a fine.

Those are all fine; so are:

Since the book was overdue, I had to pay a fine.
I had to pay a fine since the book was overdue.

In short, even though many definitions of since includes because but not thus, that doesn't imply that since can't be used to indicate consequence, in addition to cause.