I was recently offered a position... The salary is definitely higher than my current salary. Upon verbally accepting the offer, the Human Resources Generalist asked me to submit to her a copy of my pay stub from my current employer.

Is this legal?

Aren't there privacy rights revolving around this? I feel somewhat uncomfortable doing this...

Is it legal for a company to ask your former company what your former salary was?

Aren't there compliance rules that companies must follow?

Yes they can, this is merely being nice, they can merely submit a form to your employer and verfiy your job, salary and more.

They are asking for it, so it is easy you don't have to give it to them, and they don't have to hire you. So if you did not lie about your previous job, there is no problem??

After making a verbal acceptance of the offer and salary, can a company go back and retract the salary that was originally being offered to somewhat of a lower than expected salary?

What's the purpose of providing the pay stub?

Not unless you were lying about your income to them. They want to verify your employment before you actually start, often current employers are not contacted until after you start.
This is either just standard procedure, or there is a reason to believe you are not working for this company, or you did not give the correct income.