Most downloads do not SATURATE the pipe for extended periods.. When you saturate the pipe, and then try to look up something this is when you have dns issues. If you get a timeout looking for a record, its quite possible your dns client/forwarder will not ask again for a specific amount of time. If he got a timeout last time he checked because your pipes were full.
Here is the thing how much is your upload vs your download. When you download via tcp be it a large file, be it a image on a website there are acks sent back from the client that you got pieces of the tcp transmission, as you get these packets acks sent back saying got those, send more, etc. If your upload pipe gets full just sending acks, then its kind of hard to go and ask for say a dns query. So if you upload pipe is so small that it is full just sending acks when you download at high speed then sure you can have problems.
I would really look into setting up QoS so that you can setup dns to be of higher priority. And what router do you have? Its quite possible that its crap?? And it cannot handle number of users/bandwidth..
Also keep in mind normally with a http download your browser will limit the number of connections to the server and in a sense keep space open for other connections.. If your using something like downloadthemall or something to download it allows you to sat your pipe, but also can cause issues like your having because the pipe is full which you normally don't see if just using a browser to grab the file via http and using limited sessions.
Also are you wireless?? Wireless is CRAP when saturating the bandwidth available because its shared.. And very limited bandwidth, if your on G and you have over 20Mbps isp connection - even if just you, your wireless is not going to be able to maintain that sort of connection sustained -- max G is about 18 to 23mbps actual useable bandwidth while one connection is a wired, etc.
Here is the thing, if your PIPE is full, be it 10 seconds or 10 minutes - you can not expect to look up new dns, or grab other things off other sites if your pipe is full! When you stream say a video from youtube - it should NOT saturate your pipe..
Here is me watching a video on youtube -- see the way my internet bandwidth is being used
Now compare that use of bandwidth to when I saturate the pipe using downloadthemall and grabbing a LARGE file.. Notice how its almost a flat line at the MAX of my pipe..
When I try to do something when pipe is like that then yeah its going to be slow doing anything else, dns queries could quite easy fail or timeout, etc..
But as you can see while I am viewing youtube -- my ping times are normal, since I am not SATURATING my connection
So how are you downloading?? Over wireless? Are you using something other than a browser to download, have you tweaked your browser to use more sessions? Installed any other sort of tweak software to manipulate or speed up your connections?