Redmine

This is an issue with textile (the formatting used by Redmine) and not with Redmine itself. Textile's specs itself do not allow the syntax that you used as an example; see http://textile.thresholdstate.com/ as a resource for Textile syntax.

It does, however, look like Redcloth (the Textile engine Redmine uses) doesn't support the "pure HTML" syntax, e.g.:

This might be something to bring up with the Redcloth team.

I take that last part back - the Redcloth version included definitely supports the double equal sign syntax (which got munged above), but Redmine might not allow direct HTML.

I'm going to shut up now before I make any more incorrect assertions.

That means, the trac-redmine conversion produces a little problem, based on formatting information for particular text (bold).
On the other hand the help text in the description of the Help text might be incorrect too ? May be I'm wrong..

According to http://textpattern.com/faq/180/common-textile-questions

Textile 2.0, included in Textpattern 4.0.4 and higher, allows the following syntax:

A[*bold*]word -> “Aboldword”.

So Textile has got support of such a syntax.