Maximum Initial cutrent parameter of Lead-acid batteries
You're correct, you should limit the charge current to the specified initial current, even if the battery could draw more.  Above the initial current spec the battery could be damaged, or outgas dangerous amounts of flammable hydrogen gas, or it could even explode.  With a high enough charge voltage you can nearly always get the battery to take more current than the recommended initial current, so it's important to have a current limiting function. 

Most commercial chargers will limit the charge voltage to a fairly safe value, as during charging the battery impedance rises and prevents dangerous current [if you respect the max charge voltage], but there are lots of sub-standard cheap chargers out there.

From Battery University a great site for battery knowledge:

Lead acid batteries should be charged in three stages, which are 1 constant-current charge, 2 topping charge and [3] float charge. The constant-current charge applies the bulk of the charge and takes up roughly half of the required charge time; the topping charge continues at a lower charge current and provides saturation, and the float charge compensates for the loss caused by self-discharge.