No, horses don't lie in the sense we lie. But they will learn that acting one way will get their owner to react a certain way. Oh, when I swing my head around with my ears back, they stop what they're doing. Or, if I throw a kick, it makes them stop, etc. Have you every had a pet that acted sick after it was well so it would continue getting special treatment? I have. My ferret liked getting warmed up baby food so much, he realized when he ate his kibble, he wasn't getting it anymore. So he stopped eating his kibble so Mom would keep giving him soft food. Refuse one food, get another tastier food. It's not a lie, but it's seeing what they can get away with.
And no, his back wasn't the problem. My instructor checked him over, then legged me up to lay across him. He stood fine for that. Once I sat up into the riding position, he started to go. My instructor stopped him, and he stood fine with me on him while I talked to my instructor for 10 minutes.
Also I didn't teach him (on purpose or inadvertently) to start off when he's tacked. He usually has a waiting period with me before we step off, and I make him stand. I've only had him under a year. Previously, he had a gentleman who treated him as a pet, and before that, the Amish drove him (and also beat him.) I'm assuming one of them taught him to GO when he's tacked...probably the Amish with the buggy.
The biting when I was mounting was probably because I wasn't getting on, I was just bouncing and placing hand pressure on his back. He was trying to get me to go away and stop bothering him so he could grass, like he would any other horse. Also, I say rotten affectionately to him, not as in a bad thing.