You're right mayn Tobi did have a counter for Everything Minato had just like Minato told Naruto, but does that make what happened on episode 248 and 249 any less real? No it doesn't.
Minato set up a secrete barrier to stop anyone from interfering with Kushina's birth and had Hiruzen's anbu stay on guard, but Tobi countered/infiltrated it with his Space-Time Migration and killed the ANBU that were on guard.
Minato had a hirashin seal engraved into Kushina's jinchuuriki seal in order to always be by her side no matter what, but Tobi was able to seperate them by using a surprise attack and using Naruto as a hostage.
Minato tried to fight and defeat Kyubi, but Tobi was able to follow him even though he was using Hirashin and sneak up behind him with his op space-time migration.
Minato, having sensed Tobi sneaking up on him tried, used his super fast reflexes to kill Tobi with his high penetration Hirashin Kunai and then take care of Kyubi, but Tobi countered with inangibility followed by space-time migration, which forced Minato to leave the battlefield with Hirashin or get trapped in other dimension. In which case Tobi managed to prolong the Kyubi's attack on Konoha.
There are more things that could be pointed out but the moral of the story is that Tobi understood perfectly how Minato's jutsu worked and had already come prepared with counters for everything Minato had. Kushina's story and Minato's story check out perfectly, Kushina didn't lie about anything.
Tobi was miles ahead of Minato because of better space time techs and prep time, but Minato eventually caught up as the battle was prolonged and discovered Tobi's weaknesses. Plus Tobi didn't know about Hirashin version two and then lost.
Kushina didn't lie about nothing , their stories check out, just that she gave a more detailed view of the events.
Tobi lost to Minato, plain and simple, he was miles ahead and because of his failure to end th battle quickly, ended up getting exposed in the end and lost.
It seems like the basis for you saying that kushina lied is that Minato won the battle in her version of the story, but bare in mind that Minato never said that he lost either.
As for saying that Tobi just randomly stopped fighting and left, honestly, who do you hope to convince with that?
So Tobi waited for YEARS (like he said) for that opportunity but then afterwards called it a game and said 'hey, go along and seal the fox now, I'll be going home'? Please mayn.
It is obvious that he lost the battle.
But I suppose since he is still alive, he still has a chance of winning the war between him and Minato, after all, even if you lose some battles, you can still win the war.
Minato's chess pieces are in place and have started to take effect, actually, Naruto is his chest piece that he chose by sacrificing himself to seal the fox and he has prepaired that chess piece well but setting up some key mechanics in the seal, like stopping kyubi from taking over against pein, giving naruto words of advice (he set it up himself for the moment that Kyubi would win control) and sealing Kushina (set it up too as he said that Kushina had that one thing he couldn't give naruto, which was love and her chakra chains to helpo naruto become a perfect jinchuuriki).
Tobi is still alive himself and has good chest pieces too, like sasuke, nagato's rinnegan and six bijuu, the war, and edo tensei (Kabuto taught him).
I admit though that though he lost the battle, Tobi would have won the war as he has better chess pieces and is still alive to manage things, just that he is on the wrong side of plot no jutsu, lol, so we know he will lose the war too.
