Yeah, Dan's right about that. Everyone really needs to stop taking what Google says at face value and really think through the possible implications of every website tweak they make. Redirects do a ton more than kill/pass pagerank, so you can really mess up a website's performance if you pick the wrong one.
301 is still a permanent redirect, while 302 is a temporary. You're still telling search engines (all search engines, stop thinking about just Google) how they need to interpret the change. 301 means the previous page will never come back, while 302 could be used to rebuild the old page or run a short term promotion page in place of the core page.
I have a weird client that put their home page at websitename.com/product and I begged them to redirect the home page so that it resolved at websitename.com
That is pretty weird, but I see doing websitename.com/index.html as the homepage the same thing. If you go to websitename.com, does it redirect to /product? If not, then you need to put a redirect one way or another.
I think it changes a few things. . .for example, before I might be afraid to change a URL, but now, I should probably be less resistant to change urls, since, a 301 redirect won't hurt.
If you change a URL, you could still see issues; mostly related to what Dan mentioned with canonicalization. If you change a URL or URL structure, you still need Google to crawl the page to understand it's gone and pointing to a new page (if a 301 is used). You may see a temporary drop as things are getting sorted out on Google's end as well. There's also the potential that a keyword in the old URL was helping (either from an algorithmic standpoint or a CTR), so that could affect things.
There's just a lot more to think about when doing redirects than just whether PageRank will be passed. You need to make sure the strategy fits the company objectives and the new page will be more beneficial to the user.
two helpful resources -
https://moz.com/blog/301-redirection-rules-for-seo
https://support.google.com/webmasters/answer/93633?hl=en
The last thing I'll add about using a 301... If you decide to use a 301, you need to be absolutely sure the previous page will not be used again (mostly related to URL). It's a pain to get the old page reindexed once the redirect rule has been lifted. Not impossible, but expect to put in some work and for it to take time. If you think the old URL/page will be needed in the future, use a 302.