No, Nikao is exactly right, and you don't understand what he said. The argument isn't that links have to be made on related pages. We already know that links can be placed on irrelevant pages surrounded by irrelevant content, and they will still count as a positive factor in Googles algorithm. That isn't the question.
The question is whether there is a benefit of placing your link on a page surrounded by relevant content, vs placing it on a page surrounded by irrelevant content. Then the next question is, if so, is it a big enough benefit to outweigh the effort of actually placing the link on a page surrounded by relevant content.
As Nikao said, just because you CAN rank a site using link from irrelevant pages, doesn't mean that it wouldn't be better to use links from relevant pages. They might both work, and links from irrelevant pages might be enough for certain niches, but the question remains: are links from irrelevant and relevant pages treated the same/similar.
Only Google can answer 100% sure. We could test it doing side by side comparisons, but you would need hundreds of sites to come to a reasonable conclusion. The probable answer is that Google does give the links more value, so if you find yourself unable to get the ranks you want from using links on irrelevant pages, try to get more links from relevant pages.
