The point of caching is to increase performance, not specifically to reduce server load, but there is pretty obviously a relationship-- perhaps not exactly the one(s) you expect.
This is by no means a canonical answer but here are several things I can think of:
- Some kinds of caching increases memory usage.
- Caching that uses mem_cache, for example, would fall into this category. You get better performance but higher memory usage (RAM).
- Some caching increases disk usage and (maybe) disk read/writes
- Caching plugins that save the generated HTML and serve that where possible would increase the disk spaced used and (maybe) increase the disk read/writes, but that latter is pretty if-fie.
- The process of building a cache file could be somewhat server intensive.
- The plugin would need to store the generated page, compress it (maybe), save it... things like that. You have RAM, CPU, and disk writing right there. But with the caching plugin configured correctly that should be relatively rare. Badly configured, or used incorrectly to try to cache effectively un-cache-able pages, a caching plugin could be generating cache files constantly and never (rarely) using them.
So, if this host has very aggressively "thin provisioned" RAM, CPU, and/or disk space, maybe that explains it. Or if they are worried about poorly configured caching plugins, that could explain it. Overall, though, I would expect server load to go down for the same volume of traffic.
On the other side...
- Some caching plugins facilitate off-loading resources-- loading from a CDN. That should certainly reduce server load.
And a number of other hosts actually recommend the use of caching plugins.
Finally, I chafe at the use of the word "modules". Maybe it is nit-picking, but is suggests the host doesn't really know WordPress very well.