Although i am sure the author of that indoor cycling guide is good butfurther reading i see he discounts core exercises for indoor cycling as they are not needed in a class, Interestingly enough the reasons he gives for not doing hovers can be helped by do core routines.
http://www.livestrong.com/article/463891-core-workout-for-cycling/
http://bloombikeshop.com/bodyweight-exercise/
http://www.bicycling.com/training-nutrition/training-fitness/core
Actually if you read the article, the author (me) says that core training is VERY important for cyclists....just not WHILE pedaling the bike! Cyclists do not suck the abs in while riding - on the contrary, they let the belly hang so they can properly use diaphragmatic breathing and increase O2 uptake. You shouldn't hold your abs in while pedaling under the guise of "core training". Many indoor cycling instructors wrongly cue this. You aren't going to hurt your back riding a bike if you don't suck in your abs. Your intrinsic core muscles know exactly what to do to protect your back, it doesn't need to be done on a conscious level.
The reasons for not doing hovers are far more lengthy than not doing core work. The reasons for not doing hovers are because of the incorrect biomechanics. It is not how a cyclist rides a bike, because it would take her out of the correct biomechanical position to applying force to the pedal. Therefore it follows that it should not be done on an indoor bike because the laws of biomechanics do not change from a cyclist to a non-cyclist, or from outdoors to indoors*. It's even worse indoors because the bike is static and does not allow for any dissipation of energy, hence driving that energy into the joints - knees and back. Here is another article on why not to "Hover"
http://www.indoorcyclingassociation.com/public/The_How_To_Guide_for_Hovers_Indoor_Cycling_What.cfm
I actually called out Livestrong for posting an article that included how to do hovers. They ended up pulling the post because of the outcry from dozens of knowledgeable instructors who left comments.
http://www.indoorcyclingassociation.com/blog/?p=526
Recently, I was consulted in an article in the LA Times about the safe and effective way to teach (and take) indoor cycling classes, specifically calling out a popular boutique studio in NY called Soul Cycle. In addition to the silly upper body workouts while pedaling, they love to hover over at Soul Cycle.
http://articles.latimes.com/2011/nov/28/health/la-he-fitness-soulcycle-20111128
The ebook they are referring to in the article is called Keep it Real.
www.keepitrealebook.com
You should always
Keep it Real indoors, for safety and for effectiveness of the workout.The rule of thumb in any indoor cycling or Spinning® class: if you would not do it on your road bike outside, do not do it on your stationary bike inside.
* there are a few mechanical differences on a static indoor flywheel-driven fixed-geared bicycle that have an implication on how you pedal, more having to do with cadence and allowing some upper body movement to compensate for the lack of movement in the bike frame; but the same
mechanics of riding a bike outside and the same positions used on a bike outside apply indoors. Period.