How true it is? Not the faintest, but maybe someone here was in a/the Alpha design team and can say yes/no.
There's definitely a lot more playing with clock domains too though. Run this bit at half clock, etc. But you still wouldn't want to have entirely async things within an execution unit, because bringing them back in sync costs a couple clock cycles on its own.
I do wonder how the tooling used in leading edge VLSI design rates on software quality. If the open FPGA tooling community has taught us something, it's that vendor tooling is hideously inefficient and just plain bad software. If VLSI design is on the same level (and it wouldn't be surprising if it is; in fact some FPGA tooling is done by the same companies and a similar codebase), then they might be leaving performance, design time, or both on the table just because the damn P&R and timing analysis take much longer to run than they would if the software weren't terrible. Of course I'm sure they just throw more machines at the problem for high stakes chip design, but...
Just plain bad software and hilariously overengineered sure, but inefficient is a big word to throw out. I don't think any non-vendor tool has yet proven able to play in the same league, yet. It's like comparing tinycc with gcc.
Typical numbers for designs going for higher clocks (read: Pentium 4) would be 16 FO4 stages per clock. So of all you're doing is moving data from point A to point B on the chip, that still gives you quite a bit of leeway for adding buffer stages without having to add an extra cycle of latency.
Things have changed though, as other commenters have pointed out. These days everything is a lot more complicated, as you get to smaller nodes.
And if you are going to do anything useful (e.g. toggling the signal), the max frequency at which you can do it is even lower than the limit set by the propagation delay.
In any case, even TFA says the reason pretty explicitly: it's actually 4 pipelined stages, thus 4 clock cycles delay. Probably it was way too much power+area to drive the distance in one cycle.