These situations are not similar.
Although the story context is not similar, the core is still very similar. The post owner specifically asked about “forming a conjugal relationship” with a straight guy “i would assume” while she is a lesbian accepted refugee (until here everything looks very similar) the baseline here is whether or not an LGBTQ+ individual can form a “conjugal relationship” with an opposite sexual orientation individual.
According to the Supreme Court, the officer who handled the case was a “close minded” not only that but also the article specifically mentioned that this decision will open the way for many who does feel the same “only if it’s getting blocked by the officer” although i myself many cases like that. I cannot prove it hence i won’t be mentioning these but i can list some other similar stories and some verified lawyers opinion “positive” too.
The picture is pretty damn clear that it is possible and granted. However the pr application thingy does need a lawyer as i have no answer to it, not because of misrepresentation because it is not but whether or not she is allowed to do it. A lawyer is needed anyway.