It would also prohibit ISPs from modifying responses in situ - like inserting tracking beacons gifs into HTML responses or returning a custom search page (with associated ad revenue) when a DNS lookup fails.
Edit: So, with the 'if the content is legal' clause, Obama was probably referring to refusal to carry / illegal purpose court decisions. This can be applied only in very, very limited circumstances. A couple court decisions that are relevant:
* Nadel v NY Tel., 170 NYS2d 95 (1957); carrier suspected caller of using the telephone for illegal gambling transactions and terminated their service. Court ruled that service should be reinstated: the telephone company "is not at all qualified, in the absence of evidence of illegal use, to withhold from the petitioner, at will an essential and public utility."
* Shillitani v. Valentine, 53 NYS 2d 127 (1945); "a telephone company may not refuse to furnish service and facilities because of a mere suspicion or mere belief that they may be or are being used for an illegitimate end; more is required."
* People v. Brophy, 49 Cal.App.2d 15, at 33, 120 P2d 946, at 965; "public utilities and common carriers are not the censors of public or private morals, nor are they authorized or required to investigate or regulate the public or private conduct of those who seek service at their hands."