The highest I've seen the ethernet run at consistently, either personally or by people reporting numbers here, is in the range of 6-9 MB/s -- even the bottom end of that is quite a bit more than 30 Mpbs.
So no, there is no such limitation. Worth noting that it will do that while writing out through USB as well, which makes sense because the realistic data transfer speed of a USB 2.0 bus is probably 250-300 Mbps, and if the ethernet is using say 70, then writing back out at the same rate = 140 total, which yes it is capable of and will do about that in practice.
The take away, I think, is that it is not fast I/O wise by today's PC standards, but it is also atrociously slow in general by today's PC standards. It does not even stack up to most high quality modern smartphones, and it uses more power due to some lower quality components. However, it retails for $35-40 USD. The people who've made it have clearly stated their number one priority was low cost, not performance, and not low energy consumption. The reason for that is they wanted something that was easily affordable globally (as in, including the third world) for, e.g., educational institutions.
It's cheap. It's been very successful because it also (at least by now) pretty reliable, and has reasonable performance characteristics. You can run a crude desktop even on the single core models -- albeit perhaps frustrating compared to, say, your $500 laptop.
It is not:
- A replacement for a production server.
- A replacement for a desktop workstation.
- A replacement for a normal, multicore, high power computer under any conditions.
I think a lot of people are hypnotized by the low price tag and some of the things some people with a lot of savvy and expertise have gotten it to do. I think a lot of those same people have been sadly disappointed when they get it and realize what <$50 worth of parts really adds up to. You get what you pay for. It is not a miracle device from a more technologically advanced alien species. It is a clever little thing from the UK.
One thing that is unusual about it and attracts a lot of people, vs. a PC or phone, is the GPIO breakout. While adding comparable bits to a normal computer may (or in fact, may not) be possible, it is going to cost you a lot more that a Pi just for the adapters (and put much more valuable equipment at risk of damage).