PLT OF SMA INADVERTENTLY ENTERED ATA OF JXN AND HAD NMAC WITH ANOTHER SMA.

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I DEPARTED AZO VFR AT APPROX XA40 PM; CLBED TO MY REQUESTED ALT OF 3500 MSL. THE INTENDED COURSE WAS APPROX 090 FOLLOWING INTERSTATE 95 EBOUND; WITH AN ASSIGNED SQUAWK CODE; BOUND FOR ARB. AS EXPECTED; APPROX 20 MI E; AZO APCH (119.2) SUGGESTED I CONTACT LANSING ON 127.3. LANSING WAS WAITING FOR ME; AND PROMPTLY ASSIGNED ME A NEW SQUAWK. THEY COMMENTED THAT MY (RADIO) SIGNAL WAS WEAK; BUT NEVER RETURNED WITH THE EXPECTED 'RADAR CONTACT'. UNUSUAL; BUT NO PROBLEM. APPROX 10 MI LATER; I CALLED LANSING TO ASK IF I NEEDED TO CONTACT JXN TWR ABOUT TRANSITIONING THE JACKSON ATA. THE RESPONSE WAS; NO; THEY WOULD TAKE CARE OF THAT FOR ME. NO MENTION OF A WEAK SIGNAL. THE DAYS TRIP HAD TAKEN US FROM ARB; TO Y88; MLB; AZO AND BOUND BACK TO ARB. THE ENTIRE DAY; THE RADIO TFC WAS VIRTUALLY NON STOP ON ALL APCH AND CTAF FREQS. HOWEVER; SINCE SWITCHING TO LANSING; THE FREQ WAS DEAD QUIET. I COMMENTED TO MY SON ABOUT IT; BUT WASN'T CONCERNED SINCE IT WAS LATE SUNDAY AFTERNOON. XING OVER JXN SHOWED NO ACTIVITY AT THE ARPT. WE WERE APPROX 1 NM NE OF THE FIELD AT 3500 MSL FLYING A COURSE OF 090 WHEN WE SAW A SINGLE ENG; HIGH WING; FLYING A COURSE OF 360 APPROX 500 FT R ND 200 FT BELOW US! WE CLBED ABRUPTLY; BUT IT WAS OVER ALMOST IMMEDIATELY. THE OTHER ACFT GAVE NO INDICATION THAT IT EVER SAW US. THE DISTANCES ARE ESTIMATES; BUT IT WAS TOO CLOSE FOR COMFORT NO MATTER WHAT THE MEASUREMENT. AFTER REGAINING MY COMPOSURE; I CALLED LANSING AND ASKED IF THERE WERE ANY OTHER ACFT NEARBY; BECAUSE WE WERE ALMOST INVOLVED IN A MID-AIR COLLISION. THE RESPONSE WAS 'NO; WE SHOW YOU APPROX 2 NM NE OF JXN WITH NO OTHER TFC.' THIS WAS FOLLOWED BY WORDS TO THE EFFECT OF 'YOUR AT 3500 MSL AND YOU SHOULD BE AT 3000 AGL (MIN) TO CLR THE ATA.' THE INDICATION WAS THAT I HAD NOT BEEN CLRED THROUGH THE ATA. THE FIRST 2 CONVERSATIONS WERE WITH A DIFFERENT CTLR THAN THE LAST CONVERSATION. SOME 5 MINS LATER; RADAR SVC WAS TERMINATED; AS WE CONTINUED TO ANN ARBOR. ACCORDING TO MY (INST) INSTRUCTOR; HE FEELS THAT I DID NOTHING WRONG. IT IS THE ULTIMATE RESPONSIBILITY OF THE PIC TO SEE AND AVOID. VFR FLT FOLLOWING DOES NOT GUARANTEE ANYTHING; IT IS AN 'AS AVAILABLE' SVC. FURTHERMORE; IF I WASN'T CLRED THROUGH THE ATA; SOMEONE WOULD BE TALKING TO ME ABOUT MY 'TRANSGRESSION.' IN SUMMARY; I DO HAVE THE FOLLOWING CONCERNS ABOUT THE INCIDENT. IF JXN TWR KNEW THE OTHER ACFT WAS NEARBY; WOULD THEY CONTACT LANSING OR TRY TO CONTACT ME DIRECTLY? IF MY RADIO WAS HAVING PROBLEMS; AND LANSING COULDN'T REACH ME; HOW WOULD THEY REACH THE OTHER ACFT IF THEY DID SHOW IT? VIA JXN TWR; OR DIRECT BROADCAST ON THE JXN FREQ? WHAT PRECAUTIONS CAN I TAKE; AS A PLT; TO AVOID THIS SITUATION IN THE FUTURE?