It’s a bit of a cliché by now to say that Europeans are fearful of big data and its effects on their privacy, but it’s true, as a study for Vodafone’s thinktank clearly demonstrates.

The Monday report (PDF), carried out for the telco’s Institute for Society and Communications by Kantar-owned market researchers TNS Infratest, showed just under a third of the 8,000 respondents believed there were advantages to big data. Barely more than a quarter thought companies respect the privacy of their personal data.

The skepticism was particularly marked in (surprise!) Germany, where 56 percent of respondents said they deliberately avoid including personal information in emails and text messages, because they fear the privacy implications.

In a guest commentary for the study, Oxford Internet Institute professor Viktor Mayer-Schönberger called the results an “indictment of current European data protection practices” that showed people are made more reticent by complex terms and conditions and opaque processing practices.

His answer? “We could regulate the use of personal data by companies and governments, interdicting irresponsible and unaccountable behavior. We already do this in many other areas that have gotten too complex for individuals to comprehend. We don’t expect people to test themselves the medication or the food they buy.”

It is worth noting at this point that telecoms providers are in a slow-boiling battle with the Googles and Facebooks of this world, chiefly because the latter face fewer restrictions on what they can do with customers’ data. Telcos in Europe are limited in the degree to which they can monetize location data, for example, putting them at a disadvantage to their new-fangled rivals.

That said, the survey results hardly make comforting reading for Vodafone.

When it comes to the kinds of companies that people trust to properly handle their personal data, telecommunications providers rate pretty low—just 18% of respondents trust them, for example, whereas 43% trust healthcare institutions, 36% trust their employers and 33% trust banks.

However, online companies fare worse. Just 16% of respondents trust search engine companies (which in Europe means Google, as the firm has over 90% of the market), 14% trust messaging providers and a mere 11% trust social media companies—down to a negligible 7% in Germany.

These figures are scary for all kinds of companies trying to make use of Europeans’ personal data, as low trust levels mean less data. If companies are really trying to make the most of the “big data” trend, that won’t just result in fewer money-making opportunities; it could skew results and throw off predictive analysis.

But for the titans that find themselves in the crosshairs of Europe’s regulators, these fears could translate into a different kind of headache.

Margrethe Vestager, the European Commission’s competition chief, said on Sunday that her department’s antitrust probes may start taking into account the collection of large amounts of personal data.

Vestager’s competition directorate is already probing Amazon’s amzn market dominance and has charged Google goog over its alleged abuse of its market position—and that’s without delving into the data dominance issue.

“If just a few companies control the data you need to satisfy customers and cut costs, then you can give them the power to just drive rivals out of the market,” she said at the DLD innovation conference in Munich, Germany. “If a company’s use of data is so bad for competition that it outweighs the benefit, then you may have to step in to restore the level playing field.”

Given that a mere 32% of Europeans seem to see the benefits of all this data collection in the first place, firms engaging in such practices, particularly on a large scale, have a lot of convincing to do.