Why are we thinking that there would have been four founding members?
Our knowledge of UFP founders is limited to three pieces of evidence:
1) TNG "Gambit" established Vulcan as a founding member.
2) ENT "Zero Hour" had the ever-unreliable Daniels indicating that Vulcans, Andorians and Tellarites were with Archer when the latter signed the charter for the future Federation.
3) Picard's scrapbook in ST:GEN contained a newspaper clipping indicating that the founders were Earth, Vulcan, Andor, Tellar and Alpha Centauri.
However, Daniels never said that those species next to Archer were also founding members. Nor did he limit their number, except by saying that later there would be "dozens" and "hundreds" of member species, suggesting that initially less than a dozen signed. OTOH, if those four and Alpha Centauri were the original signatories to the treaty, Daniels would be correct in not mentioning Alpha Centauri because he speaks of the UFP in terms of species. According to TOS "Metamorphosis", the inhabitants of Alpha Centauri are humans (or at least Zephram Cochrane was).
But we don't have to believe in five founders, either, because Picard's scrapbook text was never shown on screen. All we really have to believe in is that Vulcan was among the founders. Not even Earth necessarily was.
As for those three stars in the modern UFP logo, they actually predate the Federation. Earth's Starfleet Command and UESPA logos have the three bright stars long before there's any inkling of an interstellar alliance in ENT. Either old Earthlings had three stars they valued above others, or then they had three virtues they depicted as stars in heraldry. Or then they just found three stars aesthetically pleasing - quite similarly to how the European Union flag officially features twelve stars for purely aesthetic reasons, and the number is completely unrelated to the number of, say, EU member nations.
Timo Saloniemi