The Creative Commons licenses make a distinction between the original material you received under the license, and the modifications you make. There are different license conditions for using the original versus how you can license your modified work.
The restriction you quote only applies to the original. You cannot take a CC-BY licensed work and, without adding anything of your own to the work, add restrictions that limit how others can use the CC-BY licensed material.
Let's look at the CC-BY-3.0 and CC-BY-4.0 variants explicitly. Their language differs, but they have equivalent passages.
The quoted section “no additional restrictions” is paraphrased from section 2.a.5.B of version 4.0 of the license. To quote it in full:
No downstream restrictions. You may not offer or impose any additional or different terms or conditions on, or apply any Effective Technological Measures to, the Licensed Material if doing so restricts exercise of the Licensed Rights by any recipient of the Licensed Material.
There are a couple of defined terms here, importantly Licensed Material. It is defined in section 1.f:
Licensed Material means the artistic or literary work, database, or other material to which the Licensor applied this Public License.
This must be contrasted to Adapted Material in section 1.a:
Adapted Material means material subject to Copyright and Similar Rights that is derived from or based upon the Licensed Material […]
For Licensed Material, adding downstream restrictions is forbidden. For Adapted Material, it is OK to choose any license as long as it doesn't conflict with the CC-BY license condition of giving attribution (section 3.a). Notably, CC-BY-SA-4.0 doesn't conflict with CC-BY-4.0.
You mentioned this license version in the question. The same argument as for version 4.0 applies, albeit with different terms.
The corresponding prohibition on downstream restrictions is in section 4.a:
You may Distribute or Publicly Perform the Work only under the terms of this License. […] You may not offer or impose any terms on the Work that restrict the terms of this License or the ability of the recipient of the Work to exercise the rights granted to that recipient under the terms of the License. […] You may not impose any effective technological measures on the Work that restrict the ability of a recipient of the Work from You to exercise the rights granted to that recipient under the terms of the License. […]
Here, the defined term is the Work which is defined in section 1.f:
"Work" means the literary and/or artistic work offered under the terms of this License […]
This must be contrasted to an Adaptation. It is defined in section 1.a:
"Adaptation" means a work based upon the Work, […]
While version 3.0 does not explicitly authorize choosing a different license for the Adaptation, it is clear that the quoted restrictions only apply to the Work. Adaptations have a different set or restrictions in section 4.b, which is just about providing attribution. The CC-BY-SA-3.0 license does not conflict with the conditions in the CC-BY-3.0 license.