Sadly, the filename doesn't appear in the link - that comes from the code/database, based on the image ID. So yes, using the ATTACH tag to link to attachments not in the current post is of limited utility - one of those "might be occasionally useful" things, rather than an exciting new discovering
On MyBB, it's slightly different. To achieve the same, you do this:
...rather than:
Code:
[ attach]64985[ /attach]
EDIT: Extra spaces added, because "ATTACH" is parsed, even in a CODE block...
And if you change "attach" to "attachment" here, it doesn't work. I've been doing a bit of reading around, and seen suggestions that "attachment" is a later addition to BBCode (and "attach" is actually a vBulletin mod?). Obviously we're running a fairly old version of vBulletin, so that might explain that one.
BTW, that's probably a good thing. One forum I lurk on recently changed to vBulletin 5, and it's radically different, and not in a good way. It's rather Javascript/JSON heavy, and a worse user experience compared to this site. I've no idea if/what their admin could do more to improve things, but it's fair to say the site owner is pretty disappointed, especially give that vBulletin is not exactly cheap!