Actually the base mount screw may be the most common culprit for a Savage bolt lock up with the front action screw being a close second offender. Most times the front and rear base mounting screws get mixed up. The front screws are shorter and the very front screw should be the shortest of all of them.
The action may close on an empty chamber fine but as soon as you load up the ejector spring with a cartridge case, the floating bolt head will move just enough to catch the now interfering screw. (believe me it doesn't take much extra length to cause this...It happened to me with a base change using the same screws in the same holes...The base was the same brand only a different color...Had me dumfounded for a while...I took off about 10 thou and everything was hunky-dory). One has to remember to also check the very front base screw for clearance to the barrel threads. Otherwise it may bottom on the barrel threads and leave you with a possibly loose base even though the screw is tight.
In the OPs case it sounds like someone other than Savage mounted the scope. The smith took care of it without charge.
My .02