Not true. My old Lumia 920 produced really incredible low-light images, and the 1020 is evidently even better (as it should be with 41mp + OIS). Don't get me wrong, I love my Note 3 and would never go back to a Lumia but the Note 3's camera definitely comes up short in some aspects compared to "some others" in the market. The camera may not be one of them, but this phone still has a very long list of very strong selling points regardless.
The 920 produced pictures with decent light in them. The image quality, however, was not great... Almost every review concluded the 920 produced soft images and sometimes struggled with focus. This is most apparent once you move the pictures off the phone to a machine with a bigger display. The HTC One also produces brighter images than a lot of phone, but its resolution affects the image quality as it cannot capture details as well as higher MP sensors.
The 1020's camera prowess is much greater because it has a HUGE fabulous sensor, glass lens, etc. and yes when you pixel bin images down from 41MP to 5MP the quality is going amazing (especially when a sensor that great is taking the images, they are still good even at 41 MP) - this is no different than resizing the Note's 13MP images down to 4MP - the quality in almost every scenario will still trump the HTC One's 4MP images, or the 8MP images from the iPhone when resized to a similar size there as well. Most tests have shows OIS in smartphones to not perform nearly as well as the hype would indicate (especially in video where software stabilization seems to yield consistently better results while still delivering smooth frame rates and avoiding frame drops/artifacts/distortions on phones like the Note 3) but I reckon the 1020's OIS is a bit better than the average smartphone. The 1020 is also a rather "slow shooter."
I noticed the iPhone [5S] does a lot of [aggressive] post processing and in low light which is clearly evident. Here is a crop from a low[er] light (but not dark, it was taken in a shopping mall) image taken on the iPhone 5S, and you can see the camera does some aggressive post processing which destroys a lot of detail in the image. If you're looking at it at a small size (like on the iPhone's screen) it looks fine, but it's clearly evident once you move the image to a real monitor and look at it at a larget size:
Then there's the issue of the iPhone taking low light images with a yellow cast over the whole image (Samsung's phones tend to balance the colors much better), and oversaturating colors even in daylight images (Yellows and Greens tend to be pumped up quite a bit). The post-processing tends to kill details even in daylight, especially in long shots.
All phones have their drawbacks as well as their benefits. It's up to the user to do a proper review for themselves before purchasing the device and decide which is better suited for their needs. I suggest giving yourself a couple weeks to play with the phones and make a few visits to a couple carrier stores before making a purchase (to rule out display model issues). It's good to let the adrenaline and anticipation run its course so that you can actually move past the hype and evaluate the purchase choices based on how the phones actually perform for you and not necessarily what you read on a website or what someone else is peddling (humans often overstate things, overhype things, push what they think is best in their opinion, have their favorite/least favorite OEMs, etc.).
As someone who does Sports and use my phone a lot to take video, there's no way the Lumia devices or the iPhone can compete with the Note 3 for that. Not only can you do the 720p super slow Mo the iPhone does, but you can also do 1080p at 60 FPS, with some fantastic quality and much better focus tracking than the iPhone. Additionally, the sound recorded by the Note 3's speaker setup blows away almost every other device on the market.
Which phone has the better camera for you depends largely (though not always completely) on how you use the camera on your phone.