Virtually no one thinks this any longer. This was the widely held belief in the early 18th century as a means to explain the difference between Scots Gaelic (which was a known Celtic [Goidelic] language) and Scots. The theory was that Pictish was a Germanic precursor to the Scots language (which is indeed Germanic), but this was based on almost 0 fact at all and Pictish is certainly not Germanic.

The reason why there has been such controversy surrounding Pictish is simply because there doesn't exist a very large body of period examples of Pictish - only some etchings on monuments and stones; and even then almost always just place/people names.

edit: I realize I misread your question a little, but it's a little confusing. Firstly, the Celtic languages ARE Indo-European. In Western Europe there is only one non-Indo-European language and it is the language isolate Basque. Secondly, the only theory I know of which places Pictish as a non-Indo-European Langauge (and therefore almost certainly an isolate) is Rhys's theory which was based entirely on the premise that we couldn't decipher one particular set of Pictish etchings. We have long since been able to interpret these etchings and have concluded they are indeed Celtic. That said, what Rhys was correct in noting (not uniquely, I might add) that many of Pictish's differences from standard Goidelic and Brittonic Celtic languages could indeed have stemmed from non-Indo-European sources in Europe before Indo-European languages had almost entirely wiped out Europe's existing languages. We will almost certainly never know for sure, but this isn't really unique to Pictish; rather it can be said for a large variety of languages - it's certainly not out of the question that non-Indo-European language characteristics account for some of the differences in Indo-European languages.

The Venerable Bede names Pictish along with Brythonic, Gaelic, Latin and English as one of the languages spoken in Britain. In the life of Columba it is mentioned he, a Gael from Dal Riatha, needed an interpreter to convert the Picts.

R.E.Howard made Picts into a caricature on how the "dark races" were pictured by Manifest Destiny ideologists. In a letter to Lovecraft he revealed he didn't actually believe they looked like that but he picked up that notion from a short story by Rudyard Kipling about the Haradrian's Wall (who made them shepherds short in stature, revealing nothing of their tongue) as well as a schoolbook from England which claimed that they haven't been necessarily Celts.