Certain subtitles show up when the player is too far away to hear the sound

Actually it seems the event is actually happening. In many cases this has helped me find mineshafts.

Confirmed for 16w06a. There is a mineshaft ~ 50 blocks away from me, horizontally. I am on level 88, and it is ~18.

Confirmed for 1.9. As @unknown noticed the minecart's subtitle does not appear when a minecart is actually moving around; the subtitle only seems to show when a minecart is rendered (whether by placing/summoning, or if the player comes within render distance of a minecart).

It seems that subtitles are playing no matter their Y position. Even if the sound is at bedrock, and you're at sea level.

Adding to your post, noticed that sometimes even though I'm only attacking the block, haven't broken it yet, subtitles display "Block Broken" when it should display "Block Breaking".
Update: Seems to be only with wood sounds...

I noticed this today as I was sailing across the ocean. I saw "minecart rolls" and decided to get out at a nearby island to try and investigate. Spent a long time tracking down nothing but I did discover the following weird behavior:
1) I only get the subtitle when crossing from X=1313 into X=1314. Very rarely it would happen while simply standing on 1314. I couldn't get it to happen at any other X coordinate. Going from 1314 to 1313 doesn't trigger it, going from 1315 to 1314 doesn't trigger it. Only from 1313 to 1314. (Addenda! Just tried something else, see note 7)
2) It only happens between Z=-82 and Z=-241 (not exactly though, it would at -82.3 but not at -82.1, and would at -241.3 but not -241.5)
3) It happens all the time while on a boat, simply crossing from 1313 to 1314 is enough to trigger it.
4) When on land, it only happens when increasing Y, eg: jumping from 1313,10,-90 to 1314,11,-90. Decreasing Y, staying the same, whatever, no subtitle: jump up a block from 1313 to 1314 (Addenda! See 6)
5) When on land, it doesn't appear until I actually touch the block at 1314. If I stand away from the block and jump up to 1314 it doesn't appear until I land. However, if I stand right next to it, pushing against the block at 1314, then it appears the instant I jump presumably because I am touching the block.
6) If I jump from 1312 to 1314 on the same Y level (or almost to 1312, like 1313.2) it triggers. It must be a jump, I must land on 1314, I can't land on 1313.9 and walk into 1314 it would seem.
7) If I sprint jump, I can go from 1312 to 1316: as soon as I land the subtitle triggers.
8) regardless of where I stand, how I cross the line, or how deep I am, it always indicates the sound is coming from the west (towards negative X), exactly west; if I rotate a little bit to the north or south the arrows indicate that it is perfectly west. I discovered this by jumping backwards from 1313 to 1314.
9) Correction, I can also get it while jumping up (increasing Y) from Z=-241 to Z=-240, along an increasing X starting at 1314. Presumably Z=-82 will do the same, and there's some maximum X that'll bound the box but I haven't gone looking yet, though it's probably around 1474 if it follows the Z coordinate pattern.

As was already suggested, I'm going to suspect that the subtitle is being displayed when the minecart is loaded: my server's view distance is 10 which seems to indicate 5 chunks loaded in either direction, so when I go from 1313 to 1314 it loads the next set of chunks with the minecart, same with the Z from -241 to -240, which means the minecart is probably somewhere at 1394,Y,-160, give or take 8, for some value of Y.
Assuming that's true (and I'll spend some time after finishing this to confirm it) the actual "bugs" then are:
1) Subtitle is displayed on chunk load even though the cart is not actually moving.
2) Subtitle is displayed on chunk load despite the fact that that's about 80m away in either the X or Z direction (or both) and regardless of Y position.
3) Subtitle appears to be linked to the landing following a jump for some reason, except in a boat.
edit:
4) Subtitle indicates minecart is in negative X direction when clearly it is not.

edit 2:
Minecart found at 1393, 38, -161
5) Subtitle is not displayed by minecart actually rolling. Subtitle is displayed when placing minecart. As per bug 4, subtitle indicates placed minecart is exactly in negative X direction even when placed due West (or any other direction)

Very nice, David Goldsmith. I also noticed that, when I am in a boat, the "minecart rolls" subtitle would appear. So, I tested it and the subtitle appears before you come to the minecart. It depends on the view-distance on the server

Confirmed for 1.11 (at least for minecarts).

In 1.11 I'm playing on a Realm with some friends and I recently made a Hopper timer that would trigger an Observer to activate a Dispenser to quickly dispense at Y 26. With Subtitles turned on it show Dispensed Item from there all the way up to Y 92 even though you stop actually hearing the sound at around Y 36.

It's a problem because we're using the realm as a team PVP right now and that Subtitle Error can give away the base my team has.

Also the random Minecart sound is a thing in the realm because I heard it out in the middle of the ocean with no land masses in sight.

Confirmed for 17w13a (and 17w14a). This also affects "Bottle smashes" and "Bat takes off"; the subtitles show up when the sounds are way out of range of the player.

Affects 1.11.2, 17w14a & 17w15a

Affects 1.12-pre2

Affects 1.12.1-pre1.

Also applies for "item dispensed"

Confirmed for 17w43a and 17w43b.

confirmed on 18w08a

Is this still an issue in 1.13-pre7?

Affects 1.13-pre8

The "minecart rolls" can be removed from the list, from MC-37557 . Affects 18w30b

I think "redstone torch fizzes" also displays from too far away, as well as "chorus flower grows" and "chorus flower withers". I'm in 1.14.4.

Affects 19w34a