I think I found my answer (still testing though) on this page: http://loveforunix.com/2014/10/14/script-to-download-tl-and-sp-for-aix-using-nim-and-s-u-m-a/
The Fixget method seems to download all the TL filesets AND the SP filesets, while SUMA only downloads the SP filesets. In order to download the TL filesets as well, you need to add the Tech Level in addition to the Service Pack in the product filters of the catalog.
This is extremely confusing and it would be nice if it was clearly documented in the BMC documentation. I'll let you know if this is working once the CUJ is done.
That was the solution. The PAJ is correct now.