Reconciliation CAN be real, but only if both parties are fully committed to it. It sounds like your H is fully committed to rugsweeping it, and maybe you're ok going along with that? You know you don't have the truth, and you seem ok about that. If you are, and you are both rugsweeping as it seems, then reconciliation can't be real in my opinion. When you sweep a problem under the carpet, nothing gets resolved and it rears it's ugly head eventually anyway, only it has the added years of bitterness and pain and probably some more incidences (I say that because people rug sweep just about everything, not just infidelity) mixed in.
If you want true R, rugsweeping isn't a viable option. It may work short term, but I've yet to see it work long term for both partners.
And living with the knowledge of an A is NOT by pushing it away, it's by dealing with it, talking about it, figuring it all out, and then it's no longer a painful issue in your life. It becomes just a footnote to the entirety of your M. I can talk about my H's infidelity now with anyone without shedding a tear, not because I push the pain away, but because I have processed it and have accepted it happened and it's part of my life and we've moved on and HEALED through it. If you don't talk about it and work on it, then how can you heal from it?