When web development really started a few years ago almost all developement was static html pages, therefore, all one really needed was to know HTML. However, the internet and development has changed. Most large commercial sites are using backend databases to get information for their website, whether they are using large commercial databases DB2, Oracle, Sybase, Informix, or using free databases like MySQL or PostgreSQL, and they are using Java Application Servers like WebSphere, Tomcat, JBOSS to deploy that data. It is assumed that the developer knows HTML, because they will be using it in displaying info in JSPs.
Database programming, itself, is probably not needed, however, you will need to know database structures (tables and rows, etc.) and SQL (select * from customers where state equals CO and Date is > 1999... and so forth) to be able to develop an application for the web if it is using data stored in a backend database.