Aaaaaah makes sense now!!!
Ok, .....
If your report was issued by the Birmingham Assay Office
http://www.anchorcert.co.uk/tanzanite.html then you can safely say that it has been independently certified and therefore what it says on the certificate is what you've got. Interestingly, as you will see from the link, their A, AA, AAA, AAAA grading is somewhat different from the grading that has typically been used
by jewellery channels. Their grading refers to saturation/intensity of the gemstone - jewellery channels used to use the AAA system to indicate quality not intensity of gemstones. So there is a difference in how the term is being applied.
IF your gemstones have been rated as AAA and an SI then that's a reasonable quality but as you can see from the link, it's not top in terms of colour intensity and clarity. So if you want to find out if you've paid a fair price you need to take that into consideration and compare like for like.
IF your report isn't an Anchorcert then the above may not apply! Sorry to be so "if" and "buts" but I'm trying to give you as much information as I can for you to benchmark against.