[Some early A3-03 receivers weren't heat treated properly and some of the early receivers were know to explode on firing, sending shrapnel and the bolt flying, causing some serious injuries and one fatality. ]
That's the first time I've heard of that, in over 45 years of hunting, shooting, and working on guns - including over a dozen Springfields.
Now, if you actually meant early, pre-WW I 1903 receivers, and not WW II 1903-A3's - then that's true,and is determined by the 1903 model's serial number. They were referred to as "low-numbered Springfields", and in no way pertain to the 03-A3.
Low numbered 1903 Springfields were those manufactured by the US Arsenal at Springfield, Mass (the original Springfield Armory) and the US Arsenal at Rock Island, IL(Rock Island Arsenal) carrying serial numbers below 800,000 only.
Those were the only two sources of production for original Model 1903 Springfield rifles.
Production was changed there at serial 800,000 from the troublesome single heat-treated receiver to a double heat-treat process, until serial 1,275,768. These make excellent sporters.
Remington made the Model 1903-A1 from 1930-39, then switched to Model 1903-A3 production, along with the Smith-CoronaTypewriter Co.
The 03-A3 design was adopted as a production cost saving device, since it used stamped non-essential parts ( trigger guard assy, mag follower) ILO milled parts, a less expensive peep ILO the barrel tangent sight, and two-groove barrels ILO the normal barrels used prior. Additional production savings were made by not finely finishing the exterior of the action & bolt/parts.
Most sporterized 03-A3's were rebarreled, if not recalibered too - but even the two groove barrels give decent hunting accuracy.
Most restocking jobs provide for only a half swing of the bolt stop/disconnect - enough to remove the bolt, but not enough to stop magazine feed, since that WW I wartime feature is no longer desired.
It's a plus, if your sporter has an aftermarket adjustable trigger installed, too - like a Timney. It was one of the best available, at that time.
$350 is a more than fair price - I've sold 03-A3 Springfields that were "sporterzed" only with the simple addition of a Bishop or Fajen monte carlo stock & a cheap scope for over $400.
Of course, if the stock's a two-piece affair, then the rifle's a British .303 Enfield - an effective hunting cartridge still popular in Canada - and only worth the money if it's been rebarreled (no military barrel markings) and has a high quality finish on both wood and metal, and quality sights. Otherwise, not worth it.