Not necessarily. Germany uses just pens and paper ballots for the election and has fairly trustworthy results. We can typically call the vote after six to eight hours, with the last votes being counted within twelve.
We do that by requiring all parties that are electable in a region to send representatives to the polling places. After voting ends, all ballots are taken to a backroom and divided into stacks. Each party representative tallies the votes in one stack, than passes the stack on to another party's representative. They tally the stack as well; if any discrepancies are found the stack is passed on to another representative and so on. Once all ballots have been tallied and everyone agrees that the count is accurate, the ballots are put into sealed containers for secure transport to the election commission and the tally is reported to them electronically. The whole process is open to public inspection so if you want to watch people count votes for eight hours on a Sunday night you can.
Since the count is parallelized over all polling places and over all parties within each polling place we can get authoritative results within hours. Typically, voting ends at 18:00 and the results are clear enough to call the election at around 22:00, with the last tallies coming in at around 02:00. There is no debate about manipulated voting machines because there aren't any voting machines. And since the parties check each others# results during the count it's assumed that the tally is fairly accurate.
Of course that only works if you have enough parties to matter; with two parties and a talking spoiler effect you're not going to be as fast. Oh, and in Germany polling places are only allowed to serve a certain number of voters by law; if there are too many voters and additional polling place has to be created. Of course that doesn't mesh with the American voting district system at all.