This proposal (or similar solutions requiring an on-chain transaction) would move funds in the channel back from user B (Bob) to user A (Alice). This is useful, because a channel may have more traffic in one direction, meaning at some point no more transactions can flow in that direction. A single on-chain transaction is preferable to the two that would be required to close and then reopen the channel.
However, to say that this is adding money to the channel is incorrect. That is not possible without reopening the channel. Let me illustrate:
Let's say that Alice and Bob each contribute 0.5 BTC to opening transaction of the channel. This means there is a total of 1 BTC in the channel to begin with:
Alice (0.5) ================== (0.5) Bob
After some time, more traffic has gone from Alice to Bob than from Bob to Alice. This means that Alice's side of the channel is depleted, but Bob's still has plenty of funds:
Alice (0.05) ================== (0.95) Bob
Now, let's say that Alice sends Bob an on-chain transaction (not over the channel), to essentially buy back some of her BTC:
on-chain
-----(0.45)---->
+--->--->--->--->--->--->--->--->---+
| |
Alice (0.5) ================== (0.5) Bob
<----(0.45)-----
over-channel
This works to rebalance the channel, but it does not add any funds to it. There is still only 1 BTC in the channel. The funds from the on-chain transaction goes into Bob's personal Bitcoin wallet, and is not on the lightning network. It does nothing to increase the size of the channel.
This technique may prove to be useful to prevent channels from becoming unbalanced, so I don't mean to imply that this is not useful. It is also important to note that a similar technique could work by using an alternate lightning route from Alice to Bob:
routed through Charlie
-----(0.45)---->
===============(Charlie)=============
| |
Alice (0.5) ================== (0.5) Bob
<----(0.45)-----
over-channel
This would eliminate the need for an on-chain transaction. However, if an alternative route exists, it would probably make more sense to leave the Alice-Bob chain unbalanced, and simply route payments along the Alice-Charlie-Bob route.