I don't know about the issue of having to request having your tubes cut and burnt versus just cut, but for my tubal, the dr. cut and burnt and didn't tell me there was even a choice. I had no idea there were different methods myself until I began researching reversals and regretting the tubal ligation with every fiber of my being. It makes me sad that there is another one of us here who has regrets over it and wants to reverse it. Just makes me feel even more that women should be counseled before having a TL, or that they should not be allowed under a certain age, or something.
Anyway, back to your question - I requested a copy of my medical records a few months ago and they were sent to me free of charge. No dr. wants to be sued for negligence if a woman has a TL and then gets pregnant and is not happy about that, so many do end up cutting and cauterizing, or burning the ends so they cannot be fused back together. Just another thing I learned after mine that I wish I had known before!
Good luck to you - my TL is basically irreversible so we are going to IVF this summer. I hope you can get yours successfully reversed!