(Feel free to copy and paste my entire response in your note back to them.)
Yes, we know exactly what causes that query: everything.
That query is called every single time WordPress is executed, period. It is the main query that loads all the "autoload" options from the options table in the database. This is done so that it doesn't have to load them all individually. The autoload options are loaded from the database into a cache in memory. Then, future attempts by the software to load options come out of that memory cache instead of hitting the database.
In other words, that query is there to REDUCE LOAD. Not increase it.
So basically, your hosting provider is full of crap. This statement: "Logs wont show anything but what people are accessing your site," is absolute BS. The logs will show WHAT FILES THEY ARE HITTING THE MOST. WordPress has multiple entry points. We need to know what's getting hit the most often in order to determine where your load problem is.
Because no matter what they say or think, that query is NOT causing load. It's a well indexed table, and requires no CPU time for the database to execute. All it's going to do is transfer some data from the database to WordPress. It doesn't have to do row scans or full searches or anything of that sort. All they are really seeing is the fact that it is the most commonly executed query and then they are assuming that it is the problem. They are mistaken, and they really need to find somebody who knows WTF they are doing instead of talking out of their asses. Somebody with actual database experience would help, but any experienced sysadmin should know better than this.
It's a damn shame too, I was planning on switching my hosting to ASO here soon, but if this is the kind of behavior they have, then I'll have to reconsider that move.