Long and overdue as usual, here's my take ... (whew)
Yes, it's okay for anyone to edit in external references for backup
If you want to put in the effort to provide sources, go for it! However, do this sparingly: only when you're certain you're supporting the author's intent.
This Meta.SO post talks about a similar conundrum, where one user basically edited in a whole answer. Quoting Shog9's response:
[...] If you're certain the edit makes the answer better, approve it.
Consider that the alternative is you rejecting the edit, leaving a crappy answer to waste future readers' time and wasting the editor's time. Seems like a bit of a high cost for some abstract ideal, don't it?
To be honest - I was writing a very different answer to this post before I read the above. But, d'oh. Yes, the "ideal" we should be striving for here is "high quality Q&A", not ... I don't know, "user1234 was handed the rules and came up with all the ideas on their own"? Posts are editable by anyone for a reason!
The edit privileges page even explicitly says one valid reason to edit is "to add related resources or hyperlinks". I don't see our backup policy as being in conflict with this; answers should be reviewed based on their content, not who edited in which parts of it. Plus, answers can be deleted or undeleted at any time, so both "DaveG added and OP kept it" and "DaveG commented and OP added" end up in the same state.
Caveats - I was reminded of the (very unpopular) "stub answer" proposal on Meta.SO. My takeaway was that the big problem with a not-fully-explained answer is that it's hard to tell why someone is arguing for it, and you can't read the author's mind to add it in accurately. We don't want to add in "bad" sources that misrepresent the OP's intent. So...
Let the OP know
If you don't have edit privileges, then the OP will always get a notification of your suggested edit. If you do have edit privileges, they will be notified if your edit is "non-trivial":
a non-trivial edit is one which changes at least 10 characters (this is using a diff algorithm, so it's not a simple add/delete; and is naturally a little fuzzy).
To be on the safe side, I suggest pinging the OP in a comment to notify them of your change, in case they disagree and want to rollback. It's also courteous as a heads-up in case readers have questions specifically about the source you added. This is one of my biggest concerns about encouraging a third party to add sources; I know I'd be very annoyed if someone edited a bad / irrelevant / misleading source into my answer and then I had to answer comments asking about it! (For instance I could see this happening easily with academic papers - someone trying to be helpful pastes in the first abstract they find, but someone more knowledgeable in the field can tell the paper doesn't really support the conclusion and questions its inclusion.)
When in doubt, don't edit! Suggest it in a comment instead.
I know there's concerns about mods deleting comments, so just to get in front of that - if you think we've deleted a legitimate suggestion for improvement, you can always ask about it. One general tip is to be neutral and explicit about the suggestion/question in your comment, like "Can you address ...?" or "I suggest adding/removing ...". I've hit this problem too! (<- Good advice from Catija there.)
Why not personal experience?
A few reasons. The biggest one being, your personal experience is definitely not why that person thought their answer was correct. So we don't want to put words in OP's mouth by implying otherwise. It might be a similar experience - but the OP is the only one who can tell us that.
This also could open the door for basically "+1 me too" edits... which is already a problem with comments (an egregious example: many deleted comments that were just saying "this is true in [my country] too!"). While it's helpful to know "this is true in many places", and you could suggest that as an edit (as in the linked comment), we don't need answers to turn into an exhaustive list of every corroborating experience.
And just to cover all the bases.. definitely don't try to edit in your own experience as if it had happened to the OP. We had a related discussion about questions, in which a user (not the OP) attempted to salvage a hypothetical question by rewriting it as if it had actually happened to OP. This really goes against the spirit of editing - edits should not change the author's intent.
Compared to questions
I think this would be analogous to how we edit off-topic questions. If there's only a minor change and/or an obvious fix, make the edit and simply let the OP know afterwards (for questions, that's often "Should I do X?" -> "How do I do X?"). If there's many possibilities and it's too unclear to be sure, better to leave a comment to suggest improvements ("You could try asking Y or Z instead").
Similarly, edit in sources that will "fix" the answer as long as you're sure they match OP's intent; if you're not sure, err on the side of leaving a comment.