Can anyone clarify this issue and point to some reliable source on this matter please?
Best way to confirm would be to email Eliteclub I guess, and ask.
I have been able to access an archived copy of Elite Club website's downloads page (some of archive.org's servers were down recently), and indeed the confusion seems to arise from the fact that the shareware version can be downloaded for free, but to use either game (Elite II or First Encounters) after the 30-day trial period they must be registered:
We have now released Frontier and First Encounters as shareware. There is a £5 registration fee which applies if you continue to play either game for more than 30 days. We strongly recommend reading the readme.txt file included with each game before playing.
As for the distribution, the included license file states that
You may without making any payment to AUTHOR make copies of the evaluation SOFTWARE as you wish; give exact copies of the original evaluation SOFTWARE to anyone; and distribute the evaluation SOFTWARE in its unmodified form via electronic means (either directly or through the posting of a copy of the SOFTWARE on the Internet, BBS's, Shareware distribution libraries, CD- ROMs, etc.) to third parties who are interested in evaluating the SOFTWARE except for the purpose of extending their evaluation period
Of course this could have been officially made void since, but I have no knowledge of such a change so far.