I had to delete the posts for being off topic, but I'd like to argue (healthily) with you on it :)
Existence of the Legendary Birds in HGSS IS very bothersome because it's completely unneccessary and it didn't make HGSS better in any way. The birds were already in Platinum, they didn't have to put them, they are obtainable in Gen IV anyway. Their inclusion was totally unneccessary (not to mention that Zapdos has the cheapest location ever and Moltres in Mt. Silver was totally unfitting, nor did anyone in the games even MENTION these birds). Instead of wasting their time on putting the birds into the game and mapping Articuno's cave, Game Freak should have programmed the Room Decoration system.
The remakes should be faithful to the original whenever possible. This is, all addition and changes should have a PURPOSE and make the game somehow better. Safari Zone, Pokeathlon or even Mewtwo (after all, this is the only way to get him in Gen IV without Pal Park) were good additions, as they had a purpose and made the games better. The Birds were a bad change because they were there just for the sake of being there. If they weren't in, it would be no lost.
They could have put Mew or Jirachi, it would be make much more sense. Why freakin' Kanto Birds (which are supposed to be in Sinnoh, are they bilocal or what)?
Though the birds were included in Platinum, you can't call their inclusion in HGSS "unnecessary". It's not like they were necessary at all in RGBY. There's no real backstory behind them, at least none that come to mind. They're legends for the sake of being legends.
Now, something I always thought- everyone says HGSS and DPPt take place at the same time. I now disagree- I believe HGSS takes place shortly before DPPt. Lookat the start of DP, they say the exploration team couldn't find the Red Gyarados anywhere- this is most likely because Ethan/Lyra had already captured/defeated the Red Gyarados. That's just one example. The fact that both Frontiers are the same in HGSS and Platinum, would mean that there has to be time difference somewhere, as it'd be impossible to have the Brains in 2 regions at the same time.
This leads on to the actual point you made- that there was no need for the Legendary Birds to be in HGSS, because they were in Platinum. A simple explanation for this, in light of my previous paragraph, is that Red never caught or battled the Legendary Birds when he travelled through Kanto, and neither did Ethan/Lyra three years later. Thus, the Birds flew to Sinnoh. That's my theory, anyway.