The time to continue construction depends on several factors. The one you mentioned is a rule of thumb, and an old one at that.
For conventional concrete with no admixtures (or only minor admixtures such as air entraining agent), concrete is expected to achieve about 70 percent of its strength in the first 7 days. Even that rule of thumb has gotten distorted with the use of ground granulated blast furnace slag cement and other admixtures such as fly ash.
To figure out how long you should wait before moving to the next phase of construction, you should have a strength gain curve for that particular mix design. If the loads being placed on the concrete do not exceed about 50 percent of the strength of the concrete at that point, it is usually acceptable to move on. That includes equipment, access, storage, and in-place construction loads.
For typical slabs on grade, the construction loads are usually light; however, you might have some anchorage considerations (anchor bolts will pull out of concrete with insufficient strength) or wedge anchors might damage the concrete when tightened...there are lots of considerations to make, so look at the curve, and figure out where you need to be for each case. As you get more familiar with it, you can wing it, but understand the concept before you do that.