They're bullshitting, though - the number of replies to a thread has no particular effect. 10 threads of 100 posts actually take up slightly more space than 1 thread of 1,000 posts, just as if you create 10 different text files with the same text on your computer, it takes up more space than the same text 10 times in one file. That doesn't have much effect, though, it's only a fraction of a percent difference in the data size.
It's not about disk space, it's about computational inefficiency in vBulletin that manifests itself when threads exceed a certain number of posts and, worse, when there are multiple threads of this length.
What slows things down is when it has to look lots of things up. Remote-linking heaps of images does that.
Remote linking images pushes the computation onto the client side. It makes things easier for vBulletin -- all it does is ship a short string of text and your browser decides whether or not to go get the data from the external source.
A search function also does that, which is why they removed it at rpg.net. If you're just looking at one thread, however long it is, it's not very demanding on the software.
Sadly, the search function in vBulletin does not look in just one thread. vBulletin is also mired in mySQL, which has all kinds of inefficiencies when dealing with multiple indices and large volumes of data, grinding to a halt on textual searches through fields with substantial data volume (bulletin boards store an abnormally large amount of data in a single field and searching within a field is not typically a priority for databases).
The number of threads and posts they have overall clutters things, because it's all stored on their server. This is why lots of forums cull old threads. But if you keep everything, well... it's just like if you keep every newspaper you ever read, pretty soon it's going to take you a long time just to find today's paper.
This is absolutely true. They should cap threads at a thousand posts and expire them after a year for on-topic sub boards and after about six days for off-topic sub boards. Tangency is the most useless and enormous tail possible to have to drag around for an RPG board.