I didn't have Deathcap that game because I had the other two 120 AP items, Zhonya's and Echo. I wanted to get a Deathcap, but the other components of my build were more useful so I never ended up trading them out. I needed Athene's for mana regen and MR, Void Staff to deal with their full-tank Gragas, and GA because I kept dying instantly to the enemy Vayne and Poppy. With the GA, they seemed to forget about me and I could hope to survive long enough for me to get my whole combo off. Otherwise, it wasn't happening.
I did not play passively at all. I was incredibly aggro (more than I actually felt safe being) even with the enemy Gragas hanging around mid. I warded and never died to his ganks, but each time they allowed Heimer to regain ground. In addition to this, I know my jungler from that game. He's a nice guy, but if there was a division lower than Bronze V, he'd be there. Guy tunnels more than Rek'Sai, feeds more than Helmet Bro, and is just as blind as Lee Sin when it comes to map awareness. I know how risky it is to gank a Heimer, so in that game I asked him to avoid mid and help the other lanes. Any other jungler, I'd have asked for help, but in this case I actually had a better chance alone.
Also, if you mean staying out of range of his turrets as 'playing passively' then I guess I was. I went in when I could and threw them away whenever my W was on CD, but my Q/E combo was the only way I could ever reach him without taking more damage than I dealt. That also caused me to go OOM really quickly even after getting Chalice, and recalling put me back at square 1, under my tower. Heimer used TP only to go back to his own lane, never go bot or top with it, and if I left lane to gank, it basically meant my own tower falling. In hindsight that might have been an acceptable sacrifice, but I didn't want to risk it. In addition, my own bot and top were doing alright and ganking would not have been of much use.
I am not denying that I could have done things better, but at the time everything I did made sense. It may seem odd or hard to believe for someone who was not there, but it can all be rationalised.