If the double download is not true, it was passed along to me by a youtuber who regularly endorses the firmware on his channel. Just repeating what he is teaching.
A YouTuber is rarely an authority on anything, even if the person is serious & reliable, he/she can get things wrong, we all do.
That's what can happen when relaying information about things you don't quite master & fully understand yourself.
And you just need to look at the number of videos telling you to clean cache & cookies before using HAN/HEN tools to realise how some myths keep being propagated despite having no basis in truth.
The basis for that myth goes back years ago when we were testing the first ps3xploit proof of concept tool, an idps dumper iirc.
Back then we had our first problems with the exploit initialization success rates, we couldn't understand why, success was somewhat random but it worked better for some than others so we asked people to test a few things among which clearing cache & cookies. It turned out it had no effect whatsoever but our suggestions went viral & all of a sudden, they were branded as prerequisites.
Later on, I realised that the exploit initialization failures are caused by a bug in the memory search js code & as expected, it was not something that clearing cache or cookies could ever help with.
The only reason why it worked better for some people was that they used a blank homepage & didn't browse at all before loading the exploit, that made specific exploit data memory alignments more likely, making them detectable by the bugged memory search function & leading to overall exploit success.
It also explains why the local/offline versions of the tools (XMB items through XMBML commands) have the best success rates..
I have been working on an improved HEN installer update these past weeks, the js memory search bug is fixed, much of the js has been rewritten, HEN initializes successfully 100% of the time.
The official HEN tools will all be updated in coming weeks, other devs will need to update their 3rd party tools if they wish to benefit from the bug fixes.
Regarding the double firmware installation, it was only a requirement for the 1st gen ps3xploit tools.
They used to patch the Flash memory for CFW installation with specific 3Mb patch files that could leave the inactive ros (there are 2 ros regions in Flash memory where CoreOS files are stored, only one is used at any given time, in other words one is active & the other is inactive) in a corrupted state if you did not do a double firmware installation first.
The inactive ros corruption could lead to certain minor issues so we recommended to always perform a double firmware installation before using the tools.
Those tools have been retired for some time now, they were superseded by the PS3 Toolset which uses standard no-fsm patch files (7Mb). The standard patch files ensure that neither ros region is left in a corrupted state, making the double firmware installation requirement obsolete.
As to PS3HEN specifically, it doesn't modify CoreOS at all (it does not write any data to the Flash memory) so there should be no risk of corruption & no need to bother with double firmware installations to prevent corruption.
Note that clearing cache/cookies or doing a double firmware installation is harmless, there is no point going into a crusade against it even if fundamentally the advice is flawed.