You're right it doesn't automatically mean they have to raise capital. But very often it does for two reasons. First they bank may well own some of its own shares and count them as realisable capital holdings due to the saleable nature of shares. As their value declines so therefore does that portion of the banks capital cushion.And given how highly leveraged banks are and how little capital they hold against vast debts often a small decline is enough to take them under the minimum.

Second most banks hold quite a ,lot of other banks debts as capital. So as the share price of other banks goes down each bank holding that debt looses capital.

Other than that the decline in share price also is just a proxy measure of other likely troubles in other assets being held – as such it doesn't make them have to raise capital but it measures how likely it is.

So you're right to be question the bald statement. Sorry. I should have been a little more cautious in how I phrased it.

Excuse my ignorance, but why would a banks share price fall require capital to be raised?