Well, I don't buy it, since ...a6 is often a necessary defensive move for black while a3 is not so necessary.

True, black loses Bb4 options but white loses his Bb5/Nb5 options too - which are more common in the theoretical lines, and both king's bishops can hide on a2/a7.

Edit:

Hmm, there's actually 20 games with 3.a3 a6 4.Nf3 Nc6 5.d4 exd4 6.Nxd4 with white scoring extremely well. Though, I suppose that's because black usually plays 6...Nxd4 or 6...d6.

But 6...Bc5 still looks OK for black, though I have to admit that having a3/a6 included here doesn't seem to harm white's chances. So it

*might* be +=

After a quick look, the only 2 instances where a3/a6 might make a difference would be:

Miles-Sorin & Miles-Hebden where black would gain the option of ...Ba7 after 13.Na4 and 10.Na4

and

possibly those cases where black goes Bb6 allowing Be3xb6,

After 7.Be3 - the only one game with a3/a6 went 7...Nxd4 8.Bxd4 Qe7 instead, and black even went on to win, though the game continuation 9.Be2 d6 10.Bxc5 dxc5 looks like a nice structural advantage for white á la the Echange Ruy - however, black got pressure on e4 pretty quick so maybe it's not that simple...

Pirttimaki,T (2295) - Nippula,T [C47]

FIN-chT FIN, 1993

1.e4 e5 2.a3 a6 3.Nf3 Nc6 4.Nc3 Nf6 5.d4 exd4 6.Nxd4 Bc5 7.Be3 Nxd4 8.Bxd4 Qe7 9.Be2 d6 10.Bxc5 dxc5 11.0-0 0-0 12.Qd3 Re8 13.Rad1 Bd7 14.f3 Rad8 15.Qe3 Bc6 16.Rfe1 h6 17.e5 Rd4 18.f4 Red8 19.Bf3 Nd5 20.Nxd5 Bxd5 21.c3 Bxf3 22.Qxf3 Rxd1 23.Rxd1 b6 24.h3 Qh4 25.Rxd8+ Qxd8 26.f5 Qh4 27.Kh2 Qe1 28.Qf4 Qe2 29.h4 a5 30.Kh3 Qxb2 31.f6 Qxc3+ 32.Kh2 Qd4 33.Qg3 g6 34.Kh1 Qe4 35.Kg1 c4 36.Qc3 c5 37.a4 Qd4+ 0-1

Ochoa de Echaguen,F (2405) - Cuevas Rodriguez,M (2200) [C47]

ESP-chT ESP (4), 1992

1.e4 e5 2.Nf3 Nc6 3.Nc3 Nf6 4.d4 exd4 5.Nxd4 Bc5 6.Be3 Nxd4 7.Bxd4 Qe7 8.Be2 d6 9.0-0 0-0 10.Bxc5 dxc5 11.Bf3 c6 12.Qe2 Qe5 13.Rad1 Be6 14.Qd3 Nd7 15.Be2 f5 16.f4 fxe4 17.Qxe4 Qxe4 18.Nxe4 Bd5 19.Nd6 b6 20.c4 Be6 21.g3 Nf6 22.f5 Bf7 23.Bf3 Bh5 24.Bxh5 Nxh5 25.g4 Nf6 26.g5 Ne8 27.Ne4 Nc7 28.Rd7 Rf7 29.Rxf7 Kxf7 30.Rd1 Ke7 31.Rd6 Ne8 32.Rxc6 Rd8 33.Re6+ Kf7 34.Re5 Rd4 35.b3 Rd1+ 36.Kg2 Ra1 37.g6+ hxg6 38.fxg6+ Kf8 39.Ng5 Rxa2+ 40.Kg3 Nf6 41.Nh7+ Kg8 42.Nxf6+ gxf6 43.Re7 Ra3 44.Kg4 Rxb3 45.h4 Rb1 46.Rxa7 1-0