Possibly - but COBOL was actually very new when some of these tapes were made according to the date range in the article, so there's a high chance (I'd bet on it) that the tapes are not in COBOL record format. BCD was implemented in the machine language in the IBM machines and so it was widely used prior to COBOL, the CDC machine involved here does not have BCD in its instructions but still provided some support for BCD operations because like many smaller computers of the era these CDCs were often used to pre/postprocess tapes also used with larger IBM machines - in an analogy to more modern architecture, it was not uncommon at the time to 'map' on an IBM mainframe (collect data from other sources, often) and then take the tapes to smaller machines to 'reduce' (totalize, etc). This allowed for using time on the very expensive IBM machines more efficiently.

Is this what they mean when they say "never admit you know COBOL"? Is that programmer you?

It's not about COBOL; it's about the operating system and hardware on which they were written. Manipulation would have been via JCL (if from a mainframe) rather than from within a program. It was typical to have a multi-file header with volume information (e.g. a unique tape ID, encoding details such as BPI and number of tracks), file details (name, creating program, record size and block size if fixed, etc.)

In the mainframe example, JCL tweaks could let you bypass any automatic label processing and get directly to the files if they are intact.

[EDIT]: I didn't see the part about "severe mould" initially; I think that would make recovery a non-starter.