Non-disjunction and trisomy 13.
Why can't this be 1st meiotic division non-disjunction as well?
It absolutely can be 1st meiotic division non-disjunction as well. Patau syndrome can occur as a result of either meiotic non-disjunction event, and furthermore a mosaic form of the disorder can occur after mitotic non-disjunction.
Non-disjunction can occur in meiosis I, but it's not necessarily the same result as non-disjunction event in meiosis II. This image helps describe the formation of the gametes from non-disjunction events.
The most obvious point is that there are more aneuploidy cells born from a meiosis I non-disjunction event than a meiosis II non-disjunction event.
Furthermore non-disjunction occurs between homologous chromosomes in meiosis I or between sister chromatids in meiosis II. Was this subtlety perhaps what your lecturers/teachers were trying to describe?
Confusion somewhere in the question perhaps.
I think the problem comes from your first diagram, which appears to be an inaccurate sketch of what trisomy 13 looks like in a karyotype. This is what trisomy 13 actually looks like:
How non-disjunction leads to a disease karyotype.
Lets pretend that the 'long' chromosomes in the first diagram of this answer are chromatids of chromosome 13. Thinking about the fusion event between gametes - the aneuploidy (n+1) gamete formed from either meiotic non-disjunction event and a normal (n) gamete could fuse to make the trisomy 13 result shown in the karyotype above; there would be three 'long' chromatids rather than two.