Is it true, and if so how did they manage it?
Yes, it is true, as proven by the book linked in Brian's answer.
As to how they managed it: computers are, as a rule of thumb getting more complex over time. Turning that around means that in the past, computers were on average simpler than today. The PDP11 reference manual has around 200 pages (with the PDP-11 being considered the smallest machine having been able to run Unix); the 8086/8088 manual clocks in at 100 pages for the CPU itself but takes 800 in total to describe additional I/O processors and other relatively important parts of the architecture. The 1993 manuals for the Pentium Family already span around 1900 pages, and well past 2000 for the IA-64 docs.
This means all aspects - the hardware itself (from CPUs over the general architecture to ancillary modules like GPUs, or even math co-processors back in the foggy past), but also the software (i.e., features expected by programmers or users), the networking, and so on and forth, got ever more complex; and at the same time, users expected the OS to handle all of that in lieu of the applications ever more.
Many of these complexities scale up exponentially in that adding one feature in one of those areas influence many of the others, thus leading to additional lines of code in many places.
So even if a completely new OS today had zero baggage in the form of backward compatibility, or having to support large numbers of historic hardware devices, it would be much larger than in the distant past simply because the system architecture (CPU, GPU, I/O, RAM, and other low-level modules, together with busses and so on) is vastly more complex on even small machines today than it was in the past.
(As a little bonus: you can run a PDP-11 emulator with the Unix v6 kernel in your browser of choice (including access to
edthe UNIX editor: Using it, you get a feeling how it is if you get the absolutely necessary only. Then extend the idea to the whole operating system. You cannot compare Linux as it is today with those ancient version of UNIX.