Should Max Heart Rate be sport dependant in cycling?
Firstly, it should be said that every reputable source recommends obtaining max HR under medical supervision only, due to inherent risks.

That is why many sites discuss various ways of estimating max HR.

From my understanding of the literature (sorry, no references to hand, I hope to add some later in the weekend), the max HR obtained from different sports ranges (from highest to lowest)


aerobics 
running
cycling
swimming


Like all generalisations, there can be exceptions, as shown by the comment from Rider_X. 

Having obtained your max HR, by measurement or estimation, you would use it calculate your training zones. 

The main risk of using a max HR figure that's too high is that you can over train. You could potentially damage your heart doing this. 

The main risk of using a max HR figure that's too low is that you'll get less benefit from your training. 

So, to answer your question, there is no benefit in using a max HR figure for cycling that was obtained from another sport.