It's true. The difference is Perl is still technically competitive (or better) than the existing alternatives. It's just not considered cool anymore.
Actually I would argue than in the niche of batch record processing on mainframes COBOL still very technically competitive. Unfortunately, unlike Perl, batch record processing on mainframes is essentially the only niche COBOL is suited for...
Perl is competitive in more areas, but many of them are not traditionally high paying or high status areas for programmers, e.g. sysadministration or data munging. Combine an aging Perl workforce with lower paying positions and you end up with unfilled positions. Banks are willing to pay good money to either train someone or hire an experienced engineer to work on their mainframe.
If you call data munging "ETL" it becomes well-paid again.
COBOL is used quite heavily for all kinds of online apps using messaging (MQSeries and others), any big database you care to name, TCP/IP, and interfacing nicely with Java (among other languages). The apps are only as poor as the programmers who write them--COBOL is not inherently limiting, and is in no way stuck in a batch record niche.
Don't laugh. Consist Software in Germany is training new people on COBOL because they still have a solid demand for maintenance. Those billions of lines ain't going away any time before the last trump sounds.
I've been there: my first job out of university in 1996 was re-writing a COBOL program that was originally written in 1972, and I'd bet it hasn't changed much since then. 24 four years between re-writes sounds about right on the COBOL timescale.