I think the "Ainge doesn't like to draft foreigners" line might not be accurate.
I went back as far as the 2004 draft.
For each pick we had, I looked at all foreign players taken in the next 10 slots. These are guys Ainge plausibly "passed" on when he had the chance to take them.
I'm disregarding guys who were early 2nd round picks we couldn't plausibly have taken with an earlier 1st because of contract/buyout issues (famously, Pekovic - and also I think Asik).
Names in parentheses indicate the player we took. Names that follow are Euros we passed on.
2004 (Jefferson). Passed on: Pozdolkine, Khryapa, Monia.
2004 (Justin Reed). Passed on: Sanikizde, Seung-jin, Lishouk.
2005 (Gerald Green). Passed on: Petro, Mahinmi.
2005 (Gomes). Passed on: Hervelle, Gortat, Slokar, Ankyol.
2006 (7th pick). Passed on: Sene, Sefolosha. (Traded for pieces later used in KG trade).
2006 (Rondo). Passed on: Rodriguez, Freeland.
2007 (5th pick). Passed on: Jianlian. (Traded for Ray Allen.)
2007 (Pruitt). Passed on: Fesenko, Barak, Yue, Gasol. (Note that Gasol was more than 10 picks later...but I know people will bring him up...in which case we also passed on Seibutis, Newley and Printezis).
2008 (Giddens). Passed on: Jawai. (See above for buyout issues on Pek and Asik).
2010 (Bradley). Passed on: None. (Tibor Pleiss and Nemjana Bjelica were the next two Euros taken.)
2010 (Harangody). Passed on: Sy.
2011 (JJJ). Passed on: none.
2011 (Moore). Passed on: Maduabum, Ngombo, Majok, Hanga.
2012 (Sully/Melo). Passed on: none. (Satoransky was the next Euro taken, in round 2).
2012 (Joseph). Passed on:Kuzmic, Karaman.
2013 (Olynyk). Passed on: Giannis, Noguiera, Schroder, Karasev, Gobert.
2013 (Iverson). Passed on: Lauvergne, Dubljevic, Timma.
2014 (Smart). Passed on: Saric, Nurkic.
2014 (Young). Passed on: Caboclo, Capela, Bogdanovic.
Summing it all up I'd say that Ainge has missed two guys (Gasol and Gortat), possibly missed another depending on how hot you are for Giannis....and skipped countless Euros taken by others later, nearly all of whom turned out to be absolute scrubs and nobodies. Even if you look at Ainge's misses they are more often domestic than foreign.
It looks less like bias and more like smart drafting to me.