I think there's a better explanation that is linked to the enforcement of situations such as "someone googles Pirate Bay and gets a link to the site". SOPA puts Google at fault for this, and I assume the enforcement mechanism could very much harm a US company (Google). Unfortunately, time ran out on the segment right as they were getting to this point.
That is probably not the only reason, but I suspect it is sufficient reason for most opposition.
NO TECHNOLOGY MANDATES.—Nothing in
title I shall be construed to impose a duty on an en-
tity described in section 102(c) or 103(c) to design
its network, technology, or service to forestall or pre-
vent acts that would actually or potentially create a
cause of action under such title, or to utilize any
particular type of technology to comply with the re-
quirements of such title.
1. A US entity does not have to redesign anything to slow or prevent infringing search results/credit card payments/etc in order to avoid liability
2. No particular type of technology must be utilized to comply: they're explicitly saying they won't require firms to "use PiracyBlocker2001 on your network" or "filter search results with the ProtectLouisVuittonsProfitMargin algorithm" or something to that effect.